mirror of
https://github.com/TorqueGameEngines/Torque3D.git
synced 2026-01-20 12:44:46 +00:00
bc9033da2e
Epoxy looks to handle the projection depth range so it behaves more like D3D, so this change was doubling up and causing problems.
1899 lines
53 KiB
C++
1899 lines
53 KiB
C++
//-----------------------------------------------------------------------------
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// Copyright (c) 2012 GarageGames, LLC
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to
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// deal in the Software without restriction, including without limitation the
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// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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// sell copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in
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// all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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// IN THE SOFTWARE.
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//-----------------------------------------------------------------------------
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#include "platform/platform.h"
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#include "math/util/frustum.h"
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#include "math/mathUtils.h"
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#include "math/mMath.h"
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#include "math/mRandom.h"
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#include "math/util/frustum.h"
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#include "platform/profiler.h"
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#include "core/tAlgorithm.h"
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namespace MathUtils
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{
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MRandomLCG sgRandom(0xdeadbeef); ///< Our random number generator.
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//-----------------------------------------------------------------------------
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bool capsuleCapsuleOverlap(const Point3F & a1, const Point3F & b1, F32 rad1, const Point3F & a2, const Point3F & b2, F32 rad2)
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{
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F32 s,t;
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Point3F c1,c2;
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F32 dist = segmentSegmentNearest(a1,b1,a2,b2,s,t,c1,c2);
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return dist <= (rad1+rad2)*(rad1+rad2);
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}
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//-----------------------------------------------------------------------------
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F32 segmentSegmentNearest(const Point3F & p1, const Point3F & q1, const Point3F & p2, const Point3F & q2, F32 & s, F32 & t, Point3F & c1, Point3F & c2)
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{
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Point3F d1 = q1-p1;
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Point3F d2 = q2-p2;
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Point3F r = p1-p2;
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F32 a = mDot(d1,d1);
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F32 e = mDot(d2,d2);
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F32 f = mDot(d2,r);
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const F32 EPSILON = 0.001f;
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if (a <= EPSILON && e <= EPSILON)
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{
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s = t = 0.0f;
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c1 = p1;
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c2 = p2;
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return mDot(c1-c2,c1-c2);
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}
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if (a <= EPSILON)
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{
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s = 0.0f;
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t = mClampF(f/e,0.0f,1.0f);
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}
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else
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{
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F32 c = mDot(d1,r);
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if (e <= EPSILON)
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{
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t = 0.0f;
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s = mClampF(-c/a,0.0f,1.0f);
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}
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else
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{
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F32 b = mDot(d1,d2);
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F32 denom = a*e-b*b;
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if (denom != 0.0f)
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s = mClampF((b*f-c*e)/denom,0.0f,1.0f);
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else
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s = 0.0f;
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F32 tnom = b*s+f;
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if (tnom < 0.0f)
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{
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t = 0.0f;
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s = mClampF(-c/a,0.0f,1.0f);
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}
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else if (tnom>e)
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{
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t = 1.0f;
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s = mClampF((b-c)/a,0.0f,1.0f);
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}
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else
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t = tnom/e;
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}
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}
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c1 = p1 + d1*s;
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c2 = p2 + d2*t;
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return mDot(c1-c2,c1-c2);
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}
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//-----------------------------------------------------------------------------
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bool capsuleSphereNearestOverlap(const Point3F & A0, const Point3F A1, F32 radA, const Point3F & B, F32 radB, F32 & t)
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{
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Point3F V = A1-A0;
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Point3F A0B = A0-B;
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F32 d1 = mDot(A0B,V);
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F32 d2 = mDot(A0B,A0B);
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F32 d3 = mDot(V,V);
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F32 R2 = (radA+radB)*(radA+radB);
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if (d2<R2)
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{
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// starting in collision state
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t=0;
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return true;
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}
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if (d3<0.01f)
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// no movement, and don't start in collision state, so no collision
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return false;
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F32 b24ac = mSqrt(d1*d1-d2*d3+d3*R2);
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F32 t1 = (-d1-b24ac)/d3;
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if (t1>0 && t1<1.0f)
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{
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t=t1;
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return true;
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}
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F32 t2 = (-d1+b24ac)/d3;
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if (t2>0 && t2<1.0f)
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{
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t=t2;
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return true;
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}
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if (t1<0 && t2>0)
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{
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t=0;
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return true;
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}
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return false;
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}
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//-----------------------------------------------------------------------------
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void vectorRotateZAxis( Point3F &vector, F32 radians )
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{
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F32 sin, cos;
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mSinCos(radians, sin, cos);
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F32 x = cos * vector.x - sin * vector.y;
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F32 y = sin * vector.x + cos * vector.y;
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vector.x = x;
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vector.y = y;
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}
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void vectorRotateZAxis( F32 radians, Point3F *vectors, U32 count )
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{
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F32 sin, cos;
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mSinCos(radians, sin, cos);
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F32 x, y;
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const Point3F *end = vectors + count;
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for ( ; vectors != end; vectors++ )
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{
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x = cos * vectors->x - sin * vectors->y;
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y = sin * vectors->x + cos * vectors->y;
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vectors->x = x;
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vectors->y = y;
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}
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}
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//-----------------------------------------------------------------------------
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void getZBiasProjectionMatrix( F32 bias, const Frustum &frustum, MatrixF *outMat, bool rotate )
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{
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Frustum temp(frustum);
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temp.setNearDist(frustum.getNearDist() + bias);
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temp.getProjectionMatrix(outMat, rotate);
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}
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//-----------------------------------------------------------------------------
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MatrixF createOrientFromDir( const Point3F &direction )
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{
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Point3F j = direction;
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Point3F k(0.0f, 0.0f, 1.0f);
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Point3F i;
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mCross( j, k, &i );
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if( i.magnitudeSafe() == 0.0f )
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{
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i.set( 0.0f, -1.0f, 0.0f );
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}
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i.normalizeSafe();
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mCross( i, j, &k );
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MatrixF mat( true );
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mat.setColumn( 0, i );
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mat.setColumn( 1, j );
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mat.setColumn( 2, k );
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return mat;
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}
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//-----------------------------------------------------------------------------
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void getMatrixFromUpVector( const VectorF &up, MatrixF *outMat )
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{
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AssertFatal( up.isUnitLength(), "MathUtils::getMatrixFromUpVector() - Up vector was not normalized!" );
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AssertFatal( outMat, "MathUtils::getMatrixFromUpVector() - Got null output matrix!" );
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AssertFatal( outMat->isAffine(), "MathUtils::getMatrixFromUpVector() - Got uninitialized matrix!" );
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VectorF forward = mPerp( up );
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VectorF right = mCross( forward, up );
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right.normalize();
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forward = mCross( up, right );
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forward.normalize();
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outMat->setColumn( 0, right );
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outMat->setColumn( 1, forward );
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outMat->setColumn( 2, up );
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}
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//-----------------------------------------------------------------------------
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void getMatrixFromForwardVector( const VectorF &forward, MatrixF *outMat )
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{
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AssertFatal( forward.isUnitLength(), "MathUtils::getMatrixFromForwardVector() - Forward vector was not normalized!" );
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AssertFatal( outMat, "MathUtils::getMatrixFromForwardVector() - Got null output matrix!" );
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AssertFatal( outMat->isAffine(), "MathUtils::getMatrixFromForwardVector() - Got uninitialized matrix!" );
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VectorF up = mPerp( forward );
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VectorF right = mCross( forward, up );
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right.normalize();
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up = mCross( right, forward );
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up.normalize();
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outMat->setColumn( 0, right );
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outMat->setColumn( 1, forward );
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outMat->setColumn( 2, up );
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}
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//-----------------------------------------------------------------------------
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Point3F randomDir( const Point3F &axis, F32 thetaAngleMin, F32 thetaAngleMax,
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F32 phiAngleMin, F32 phiAngleMax )
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{
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MatrixF orient = createOrientFromDir( axis );
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Point3F axisx;
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orient.getColumn( 0, &axisx );
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F32 theta = (thetaAngleMax - thetaAngleMin) * sgRandom.randF() + thetaAngleMin;
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F32 phi = (phiAngleMax - phiAngleMin) * sgRandom.randF() + phiAngleMin;
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// Both phi and theta are in degs. Create axis angles out of them, and create the
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// appropriate rotation matrix...
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AngAxisF thetaRot(axisx, theta * (M_PI_F / 180.0f));
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AngAxisF phiRot(axis, phi * (M_PI_F / 180.0f));
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Point3F ejectionAxis = axis;
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MatrixF temp(true);
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thetaRot.setMatrix(&temp);
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temp.mulP(ejectionAxis);
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phiRot.setMatrix(&temp);
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temp.mulP(ejectionAxis);
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return ejectionAxis;
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}
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//-----------------------------------------------------------------------------
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Point3F randomPointInSphere( F32 radius )
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{
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AssertFatal( radius > 0.0f, "MathUtils::randomPointInRadius - radius must be positive" );
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#define MAX_TRIES 20
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Point3F out;
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F32 radiusSq = radius * radius;
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for ( S32 i = 0; i < MAX_TRIES; i++ )
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{
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out.x = sgRandom.randF(-radius,radius);
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out.y = sgRandom.randF(-radius,radius);
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out.z = sgRandom.randF(-radius,radius);
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if ( out.lenSquared() < radiusSq )
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return out;
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}
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AssertFatal( false, "MathUtils::randomPointInRadius - something is wrong, should not fail this many times." );
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return Point3F::Zero;
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}
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//-----------------------------------------------------------------------------
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Point2F randomPointInCircle( F32 radius )
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{
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AssertFatal( radius > 0.0f, "MathUtils::randomPointInRadius - radius must be positive" );
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#define MAX_TRIES 20
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Point2F out;
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F32 radiusSq = radius * radius;
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for ( S32 i = 0; i < MAX_TRIES; i++ )
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{
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out.x = sgRandom.randF(-radius,radius);
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out.y = sgRandom.randF(-radius,radius);
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if ( out.lenSquared() < radiusSq )
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return out;
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}
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AssertFatal( false, "MathUtils::randomPointInRadius - something is wrong, should not fail this many times." );
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return Point2F::Zero;
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}
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//-----------------------------------------------------------------------------
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void getAnglesFromVector( const VectorF &vec, F32 &yawAng, F32 &pitchAng )
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{
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yawAng = mAtan2( vec.x, vec.y );
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if( yawAng < 0.0f )
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yawAng += M_2PI_F;
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if( mFabs(vec.x) > mFabs(vec.y) )
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pitchAng = mAtan2( mFabs(vec.z), mFabs(vec.x) );
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else
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pitchAng = mAtan2( mFabs(vec.z), mFabs(vec.y) );
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if( vec.z < 0.0f )
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pitchAng = -pitchAng;
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}
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//-----------------------------------------------------------------------------
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void getVectorFromAngles( VectorF &vec, F32 yawAng, F32 pitchAng )
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{
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VectorF pnt( 0.0f, 1.0f, 0.0f );
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EulerF rot( -pitchAng, 0.0f, 0.0f );
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MatrixF mat( rot );
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rot.set( 0.0f, 0.0f, yawAng );
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MatrixF mat2( rot );
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mat.mulV( pnt );
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mat2.mulV( pnt );
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vec = pnt;
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}
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//-----------------------------------------------------------------------------
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void transformBoundingBox(const Box3F &sbox, const MatrixF &mat, const Point3F scale, Box3F &dbox)
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{
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Point3F center;
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// set transformed center...
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sbox.getCenter(¢er);
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center.convolve(scale);
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mat.mulP(center);
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dbox.minExtents = center;
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dbox.maxExtents = center;
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Point3F val;
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for(U32 ix=0; ix<2; ix++)
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{
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if(ix & 0x1)
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val.x = sbox.minExtents.x;
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else
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val.x = sbox.maxExtents.x;
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for(U32 iy=0; iy<2; iy++)
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{
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if(iy & 0x1)
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val.y = sbox.minExtents.y;
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else
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val.y = sbox.maxExtents.y;
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for(U32 iz=0; iz<2; iz++)
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{
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if(iz & 0x1)
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val.z = sbox.minExtents.z;
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else
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val.z = sbox.maxExtents.z;
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Point3F v1, v2;
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v1 = val;
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v1.convolve(scale);
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mat.mulP(v1, &v2);
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dbox.minExtents.setMin(v2);
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dbox.maxExtents.setMax(v2);
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}
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}
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}
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}
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//-----------------------------------------------------------------------------
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bool mProjectWorldToScreen( const Point3F &in,
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Point3F *out,
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const RectI &view,
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const MatrixF &world,
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const MatrixF &projection )
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{
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MatrixF worldProjection = projection;
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worldProjection.mul(world);
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return mProjectWorldToScreen( in, out, view, worldProjection );
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}
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//-----------------------------------------------------------------------------
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bool mProjectWorldToScreen( const Point3F &in,
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Point3F *out,
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const RectI &view,
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const MatrixF &worldProjection )
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{
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Point4F temp(in.x,in.y,in.z,1.0f);
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worldProjection.mul(temp);
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// Perform the perspective division. For orthographic
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// projections, temp.w will be 1.
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temp.x /= temp.w;
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temp.y /= temp.w;
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temp.z /= temp.w;
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// Take the normalized device coordinates (NDC) and transform them
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// into device coordinates.
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out->x = (temp.x + 1.0f) / 2.0f * view.extent.x + view.point.x;
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out->y = (1.0f - temp.y) / 2.0f * view.extent.y + view.point.y;
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out->z = temp.z;
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if ( out->z < 0.0f || out->z > 1.0f ||
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out->x < (F32)view.point.x || out->x > (F32)view.point.x + (F32)view.extent.x ||
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out->y < (F32)view.point.y || out->y > (F32)view.point.y + (F32)view.extent.y )
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return false;
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return true;
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}
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//-----------------------------------------------------------------------------
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void mProjectScreenToWorld( const Point3F &in,
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Point3F *out,
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const RectI &view,
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const MatrixF &world,
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const MatrixF &projection,
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F32 zfar,
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F32 znear )
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{
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MatrixF invWorldProjection = projection;
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invWorldProjection.mul(world);
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invWorldProjection.inverse();
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Point3F vec;
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vec.x = (in.x - view.point.x) * 2.0f / view.extent.x - 1.0f;
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vec.y = -(in.y - view.point.y) * 2.0f / view.extent.y + 1.0f;
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vec.z = (znear + in.z * (zfar - znear))/zfar;
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invWorldProjection.mulV(vec);
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vec *= 1.0f + in.z * zfar;
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invWorldProjection.getColumn(3, out);
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(*out) += vec;
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}
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//-----------------------------------------------------------------------------
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bool pointInPolygon( const Point2F *verts, U32 vertCount, const Point2F &testPt )
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{
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U32 i, j, c = 0;
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for ( i = 0, j = vertCount-1; i < vertCount; j = i++ )
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{
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if ( ( ( verts[i].y > testPt.y ) != ( verts[j].y > testPt.y ) ) &&
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( testPt.x < ( verts[j].x - verts[i].x ) *
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( testPt.y - verts[i].y ) /
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( verts[j].y - verts[i].y ) + verts[i].x ) )
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c = !c;
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}
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return c != 0;
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}
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//-----------------------------------------------------------------------------
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F32 mTriangleDistance( const Point3F &A, const Point3F &B, const Point3F &C, const Point3F &P, IntersectInfo* info )
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{
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Point3F diff = A - P;
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Point3F edge0 = B - A;
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Point3F edge1 = C - A;
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F32 a00 = edge0.lenSquared();
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F32 a01 = mDot( edge0, edge1 );
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F32 a11 = edge1.lenSquared();
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F32 b0 = mDot( diff, edge0 );
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F32 b1 = mDot( diff, edge1 );
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F32 c = diff.lenSquared();
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F32 det = mFabs(a00*a11-a01*a01);
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F32 s = a01*b1-a11*b0;
|
|
F32 t = a01*b0-a00*b1;
|
|
F32 sqrDistance;
|
|
|
|
if (s + t <= det)
|
|
{
|
|
if (s < 0.0f)
|
|
{
|
|
if (t < 0.0f) // region 4
|
|
{
|
|
if (b0 < 0.0f)
|
|
{
|
|
t = 0.0f;
|
|
if (-b0 >= a00)
|
|
{
|
|
s = 1.0f;
|
|
sqrDistance = a00 + (2.0f)*b0 + c;
|
|
}
|
|
else
|
|
{
|
|
s = -b0/a00;
|
|
sqrDistance = b0*s + c;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
s = 0.0f;
|
|
if (b1 >= 0.0f)
|
|
{
|
|
t = 0.0f;
|
|
sqrDistance = c;
|
|
}
|
|
else if (-b1 >= a11)
|
|
{
|
|
t = 1.0f;
|
|
sqrDistance = a11 + 2.0f*b1 + c;
|
|
}
|
|
else
|
|
{
|
|
t = -b1/a11;
|
|
sqrDistance = b1*t + c;
|
|
}
|
|
}
|
|
}
|
|
else // region 3
|
|
{
|
|
s = 0.0f;
|
|
if (b1 >= 0.0f)
|
|
{
|
|
t = 0.0f;
|
|
sqrDistance = c;
|
|
}
|
|
else if (-b1 >= a11)
|
|
{
|
|
t = 1.0f;
|
|
sqrDistance = a11 + 2.0f*b1 + c;
|
|
}
|
|
else
|
|
{
|
|
t = -b1/a11;
|
|
sqrDistance = b1*t + c;
|
|
}
|
|
}
|
|
}
|
|
else if (t < 0.0f) // region 5
|
|
{
|
|
t = 0.0f;
|
|
if (b0 >= 0.0f)
|
|
{
|
|
s = 0.0f;
|
|
sqrDistance = c;
|
|
}
|
|
else if (-b0 >= a00)
|
|
{
|
|
s = 1.0f;
|
|
sqrDistance = a00 + 2.0f*b0 + c;
|
|
}
|
|
else
|
|
{
|
|
s = -b0/a00;
|
|
sqrDistance = b0*s + c;
|
|
}
|
|
}
|
|
else // region 0
|
|
{
|
|
// minimum at interior point
|
|
F32 invDet = 1.0f / det;
|
|
s *= invDet;
|
|
t *= invDet;
|
|
sqrDistance = s * (a00*s + a01*t + 2.0f*b0) +
|
|
t * (a01*s + a11*t + 2.0f*b1) + c;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
F32 tmp0, tmp1, numer, denom;
|
|
|
|
if (s < 0.0f) // region 2
|
|
{
|
|
tmp0 = a01 + b0;
|
|
tmp1 = a11 + b1;
|
|
if (tmp1 > tmp0)
|
|
{
|
|
numer = tmp1 - tmp0;
|
|
denom = a00 - 2.0f*a01 + a11;
|
|
if (numer >= denom)
|
|
{
|
|
s = 1.0f;
|
|
t = 0.0f;
|
|
sqrDistance = a00 + 2.0f*b0 + c;
|
|
}
|
|
else
|
|
{
|
|
s = numer/denom;
|
|
t = 1.0f - s;
|
|
sqrDistance = s * (a00*s + a01*t + 2.0f*b0) +
|
|
t * (a01*s + a11*t + 2.0f*b1) + c;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
s = 0.0f;
|
|
if (tmp1 <= 0.0f)
|
|
{
|
|
t = 1.0f;
|
|
sqrDistance = a11 + 2.0f*b1 + c;
|
|
}
|
|
else if (b1 >= 0.0f)
|
|
{
|
|
t = 0.0f;
|
|
sqrDistance = c;
|
|
}
|
|
else
|
|
{
|
|
t = -b1/a11;
|
|
sqrDistance = b1*t + c;
|
|
}
|
|
}
|
|
}
|
|
else if (t < 0.0f) // region 6
|
|
{
|
|
tmp0 = a01 + b1;
|
|
tmp1 = a00 + b0;
|
|
if (tmp1 > tmp0)
|
|
{
|
|
numer = tmp1 - tmp0;
|
|
denom = a00 - 2.0f*a01 + a11;
|
|
if (numer >= denom)
|
|
{
|
|
t = 1.0f;
|
|
s = 0.0f;
|
|
sqrDistance = a11 + 2.0f*b1 + c;
|
|
}
|
|
else
|
|
{
|
|
t = numer/denom;
|
|
s = 1.0f - t;
|
|
sqrDistance = s * (a00*s + a01*t + 2.0f*b0) +
|
|
t * (a01*s + a11*t + 2.0f*b1) + c;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
t = 0.0f;
|
|
if (tmp1 <= 0.0f)
|
|
{
|
|
s = 1.0f;
|
|
sqrDistance = a00 + 2.0f*b0 + c;
|
|
}
|
|
else if (b0 >= 0.0f)
|
|
{
|
|
s = 0.0f;
|
|
sqrDistance = c;
|
|
}
|
|
else
|
|
{
|
|
s = -b0/a00;
|
|
sqrDistance = b0*s + c;
|
|
}
|
|
}
|
|
}
|
|
else // region 1
|
|
{
|
|
numer = a11 + b1 - a01 - b0;
|
|
if (numer <= 0.0f)
|
|
{
|
|
s = 0.0f;
|
|
t = 1.0f;
|
|
sqrDistance = a11 + 2.0f*b1 + c;
|
|
}
|
|
else
|
|
{
|
|
denom = a00 - 2.0f*a01 + a11;
|
|
if (numer >= denom)
|
|
{
|
|
s = 1.0f;
|
|
t = 0.0f;
|
|
sqrDistance = a00 + 2.0f*b0 + c;
|
|
}
|
|
else
|
|
{
|
|
s = numer/denom;
|
|
t = 1.0f - s;
|
|
sqrDistance = s * (a00*s + a01*t + 2.0f*b0) +
|
|
t * (a01*s + a11*t + 2.0f*b1) + c;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// account for numerical round-off error
|
|
if (sqrDistance < 0.0f)
|
|
sqrDistance = 0.0f;
|
|
|
|
// This also calculates the barycentric coordinates and the closest point!
|
|
//m_kClosestPoint0 = P;
|
|
//m_kClosestPoint1 = A + s*edge0 + t*edge1;
|
|
//m_afTriangleBary[1] = s;
|
|
//m_afTriangleBary[2] = t;
|
|
//m_afTriangleBary[0] = (Real)1.0 - fS - fT;
|
|
if(info)
|
|
{
|
|
info->segment.p0 = P;
|
|
info->segment.p1 = A + s*edge0 + t*edge1;
|
|
info->bary.x = s;
|
|
info->bary.y = t;
|
|
info->bary.z = 1.0f - s - t;
|
|
}
|
|
|
|
return sqrDistance;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
Point3F mTriangleNormal( const Point3F &a, const Point3F &b, const Point3F &c )
|
|
{
|
|
// Vector from b to a.
|
|
const F32 ax = a.x-b.x;
|
|
const F32 ay = a.y-b.y;
|
|
const F32 az = a.z-b.z;
|
|
// Vector from b to c.
|
|
const F32 cx = c.x-b.x;
|
|
const F32 cy = c.y-b.y;
|
|
const F32 cz = c.z-b.z;
|
|
|
|
Point3F n;
|
|
|
|
// This is an in-line cross product.
|
|
n.x = ay*cz - az*cy;
|
|
n.y = az*cx - ax*cz;
|
|
n.z = ax*cy - ay*cx;
|
|
m_point3F_normalize( (F32*)(&n) );
|
|
|
|
return n;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
Point3F mClosestPointOnSegment( const Point3F &a, const Point3F &b, const Point3F &p )
|
|
{
|
|
Point3F c = p - a; // Vector from a to Point
|
|
Point3F v = (b - a);
|
|
F32 d = v.len(); // Length of the line segment
|
|
v.normalize(); // Unit Vector from a to b
|
|
F32 t = mDot( v, c ); // Intersection point Distance from a
|
|
|
|
// Check to see if the point is on the line
|
|
// if not then return the endpoint
|
|
if(t < 0) return a;
|
|
if(t > d) return b;
|
|
|
|
// get the distance to move from point a
|
|
v *= t;
|
|
|
|
// move from point a to the nearest point on the segment
|
|
return a + v;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void mShortestSegmentBetweenLines( const Line &line0, const Line &line1, LineSegment *outSegment )
|
|
{
|
|
// compute intermediate parameters
|
|
Point3F w0 = line0.origin - line1.origin;
|
|
F32 a = mDot( line0.direction, line0.direction );
|
|
F32 b = mDot( line0.direction, line1.direction );
|
|
F32 c = mDot( line1.direction, line1.direction );
|
|
F32 d = mDot( line0.direction, w0 );
|
|
F32 e = mDot( line1.direction, w0 );
|
|
|
|
F32 denom = a*c - b*b;
|
|
|
|
if ( denom > -0.001f && denom < 0.001f )
|
|
{
|
|
outSegment->p0 = line0.origin;
|
|
outSegment->p1 = line1.origin + (e/c)*line1.direction;
|
|
}
|
|
else
|
|
{
|
|
outSegment->p0 = line0.origin + ((b*e - c*d)/denom)*line0.direction;
|
|
outSegment->p1 = line1.origin + ((a*e - b*d)/denom)*line1.direction;
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
U32 greatestCommonDivisor( U32 u, U32 v )
|
|
{
|
|
// http://en.wikipedia.org/wiki/Binary_GCD_algorithm
|
|
|
|
S32 shift;
|
|
|
|
/* GCD(0,x) := x */
|
|
if (u == 0 || v == 0)
|
|
return u | v;
|
|
|
|
/* Left shift := lg K, where K is the greatest power of 2
|
|
dividing both u and v. */
|
|
for (shift = 0; ((u | v) & 1) == 0; ++shift) {
|
|
u >>= 1;
|
|
v >>= 1;
|
|
}
|
|
|
|
while ((u & 1) == 0)
|
|
u >>= 1;
|
|
|
|
/* From here on, u is always odd. */
|
|
do {
|
|
while ((v & 1) == 0) /* Loop X */
|
|
v >>= 1;
|
|
|
|
/* Now u and v are both odd, so diff(u, v) is even.
|
|
Let u = min(u, v), v = diff(u, v)/2. */
|
|
if (u < v) {
|
|
v -= u;
|
|
} else {
|
|
U32 diff = u - v;
|
|
u = v;
|
|
v = diff;
|
|
}
|
|
v >>= 1;
|
|
} while (v != 0);
|
|
|
|
return u << shift;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool mLineTriangleCollide( const Point3F &p1, const Point3F &p2,
|
|
const Point3F &t1, const Point3F &t2, const Point3F &t3,
|
|
Point3F *outUVW, F32 *outT )
|
|
{
|
|
VectorF ab = t2 - t1;
|
|
VectorF ac = t3 - t1;
|
|
VectorF qp = p1 - p2;
|
|
|
|
// Compute triangle normal. Can be precalculated or cached if
|
|
// intersecting multiple segments against the same triangle
|
|
VectorF n = mCross( ab, ac );
|
|
|
|
// Compute denominator d. If d <= 0, segment is parallel to or points
|
|
// away from triangle, so exit early
|
|
F32 d = mDot( qp, n );
|
|
if ( d <= 0.0f )
|
|
return false;
|
|
|
|
// Compute intersection t value of pq with plane of triangle. A ray
|
|
// intersects if 0 <= t. Segment intersects iff 0 <= t <= 1. Delay
|
|
// dividing by d until intersection has been found to pierce triangle
|
|
VectorF ap = p1 - t1;
|
|
F32 t = mDot( ap, n );
|
|
if ( t < 0.0f )
|
|
return false;
|
|
if ( t > d )
|
|
return false; // For segment; exclude this code line for a ray test
|
|
|
|
// Compute barycentric coordinate components and test if within bounds
|
|
VectorF e = mCross( qp, ap );
|
|
F32 v = mDot( ac, e );
|
|
if ( v < 0.0f || v > d )
|
|
return false;
|
|
F32 w = -mDot( ab, e );
|
|
if ( w < 0.0f || v + w > d )
|
|
return false;
|
|
|
|
// Segment/ray intersects triangle. Perform delayed division and
|
|
// compute the last barycentric coordinate component
|
|
const F32 ood = 1.0f / d;
|
|
|
|
if ( outT )
|
|
*outT = t * ood;
|
|
|
|
if ( outUVW )
|
|
{
|
|
v *= ood;
|
|
w *= ood;
|
|
outUVW->set( 1.0f - v - w, v, w );
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool mRayQuadCollide( const Quad &quad,
|
|
const Ray &ray,
|
|
Point2F *outUV,
|
|
F32 *outT )
|
|
{
|
|
static const F32 eps = F32(10e-6);
|
|
|
|
// Rejects rays that are parallel to Q, and rays that intersect the plane of
|
|
// Q either on the left of the line V00V01 or on the right of the line V00V10.
|
|
|
|
// p01-----eXX-----p11
|
|
// ^ . ^ |
|
|
// | . |
|
|
// e03 e02 eXX
|
|
// | . |
|
|
// | . |
|
|
// p00-----e01---->p10
|
|
|
|
VectorF e01 = quad.p10 - quad.p00;
|
|
VectorF e03 = quad.p01 - quad.p00;
|
|
|
|
// If the ray is perfectly perpendicular to e03, which
|
|
// represents the entire planes tangent, then the
|
|
// result of this cross product (P) will equal e01
|
|
// If it is parallel it will result in a vector opposite e01.
|
|
|
|
// If the ray is heading DOWN the cross product will point to the RIGHT
|
|
// If the ray is heading UP the cross product will point to the LEFT
|
|
// We do not reject based on this though...
|
|
//
|
|
// In either case cross product will be more parallel to e01 the more
|
|
// perpendicular the ray is to e03, and it will be more perpendicular to
|
|
// e01 the more parallel it is to e03.
|
|
VectorF P = mCross(ray.direction, e03);
|
|
|
|
// det can be seen as 'the amount of vector e01 in the direction P'
|
|
F32 det = mDot(e01, P);
|
|
|
|
// Take a Abs of the dot because we do not care if the ray is heading up or down,
|
|
// but if it is perfectly parallel to the quad we want to reject it.
|
|
if ( mFabs(det) < eps )
|
|
return false;
|
|
|
|
F32 inv_det = 1.0f / det;
|
|
|
|
VectorF T = ray.origin - quad.p00;
|
|
|
|
// alpha can be seen as 'the amount of vector T in the direction P'
|
|
// T is a vector up from the quads corner point 00 to the ray's origin.
|
|
// P is the cross product of the ray and e01, which should be "roughly"
|
|
// parallel with e03 but might be of either positive or negative magnitude.
|
|
F32 alpha = mDot(T, P) * inv_det;
|
|
if ( alpha < 0.0f )
|
|
return false;
|
|
|
|
// if (alpha > real(1.0)) return false; // Uncomment if VR is used.
|
|
|
|
// The cross product of T and e01 should be roughly parallel to e03
|
|
// and of either positive or negative magnitude.
|
|
VectorF Q = mCross(T, e01);
|
|
F32 beta = mDot(ray.direction, Q) * inv_det;
|
|
if ( beta < 0.0f )
|
|
return false;
|
|
|
|
// if (beta > real(1.0)) return false; // Uncomment if VR is used.
|
|
|
|
if ( alpha + beta > 1.0f )
|
|
//if ( false )
|
|
{
|
|
// Rejects rays that intersect the plane of Q either on the
|
|
// left of the line V11V10 or on the right of the line V11V01.
|
|
|
|
VectorF e23 = quad.p01 - quad.p11;
|
|
VectorF e21 = quad.p10 - quad.p11;
|
|
VectorF P_prime = mCross(ray.direction, e21);
|
|
F32 det_prime = mDot(e23, P_prime);
|
|
if ( mFabs(det_prime) < eps)
|
|
return false;
|
|
F32 inv_det_prime = 1.0f / det_prime;
|
|
VectorF T_prime = ray.origin - quad.p11;
|
|
F32 alpha_prime = mDot(T_prime, P_prime) * inv_det_prime;
|
|
if (alpha_prime < 0.0f)
|
|
return false;
|
|
VectorF Q_prime = mCross(T_prime, e23);
|
|
F32 beta_prime = mDot(ray.direction, Q_prime) * inv_det_prime;
|
|
if (beta_prime < 0.0f)
|
|
return false;
|
|
}
|
|
|
|
// Compute the ray parameter of the intersection point, and
|
|
// reject the ray if it does not hit Q.
|
|
|
|
F32 t = mDot(e03, Q) * inv_det;
|
|
if ( t < 0.0f )
|
|
return false;
|
|
|
|
|
|
// Compute the barycentric coordinates of the fourth vertex.
|
|
// These do not depend on the ray, and can be precomputed
|
|
// and stored with the quadrilateral.
|
|
|
|
F32 alpha_11, beta_11;
|
|
VectorF e02 = quad.p11 - quad.p00;
|
|
VectorF n = mCross(e01, e03);
|
|
|
|
if ( mFabs(n.x) >= mFabs(n.y) &&
|
|
mFabs(n.x) >= mFabs(n.z) )
|
|
{
|
|
alpha_11 = ( e02.y * e03.z - e02.z * e03.y ) / n.x;
|
|
beta_11 = ( e01.y * e02.z - e01.z * e02.y ) / n.x;
|
|
}
|
|
else if ( mFabs(n.y) >= mFabs(n.x) &&
|
|
mFabs(n.y) >= mFabs(n.z) )
|
|
{
|
|
alpha_11 = ((e02.z * e03.x) - (e02.x * e03.z)) / n.y;
|
|
beta_11 = ((e01.z * e02.x) - (e01.x * e02.z)) / n.y;
|
|
}
|
|
else
|
|
{
|
|
alpha_11 = ((e02.x * e03.y) - (e02.y * e03.x)) / n.z;
|
|
beta_11 = ((e01.x * e02.y) - (e01.y * e02.x)) / n.z;
|
|
}
|
|
|
|
// Compute the bilinear coordinates of the intersection point.
|
|
|
|
F32 u,v;
|
|
|
|
if ( mFabs(alpha_11 - 1.0f) < eps)
|
|
{
|
|
// Q is a trapezium.
|
|
u = alpha;
|
|
if ( mFabs(beta_11 - 1.0f) < eps)
|
|
v = beta; // Q is a parallelogram.
|
|
else
|
|
v = beta / ((u * (beta_11 - 1.0f)) + 1.0f); // Q is a trapezium.
|
|
}
|
|
else if ( mFabs(beta_11 - 1.0f) < eps)
|
|
{
|
|
// Q is a trapezium.
|
|
v = beta;
|
|
u = alpha / ((v * (alpha_11 - 1.0f)) + 1.0f);
|
|
}
|
|
else
|
|
{
|
|
F32 A = 1.0f - beta_11;
|
|
F32 B = (alpha * (beta_11 - 1.0f))
|
|
- (beta * (alpha_11 - 1.0f)) - 1.0f;
|
|
F32 C = alpha;
|
|
F32 D = (B * B) - (4.0f * A * C);
|
|
F32 Q = -0.5f * (B + (B < 0.0f ? -1.0f : 1.0f) ) * mSqrt(D);
|
|
u = Q / A;
|
|
if ((u < 0.0f) || (u > 1.0f)) u = C / Q;
|
|
v = beta / ((u * (beta_11 - 1.0f)) + 1.0f);
|
|
}
|
|
|
|
if ( outUV )
|
|
outUV->set( u, v );
|
|
if ( outT )
|
|
*outT = t;
|
|
|
|
return true;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// Used by sortQuadWindingOrder.
|
|
struct QuadSortPoint
|
|
{
|
|
U32 id;
|
|
F32 theta;
|
|
};
|
|
|
|
// Used by sortQuadWindingOrder.
|
|
S32 QSORT_CALLBACK cmpAngleAscending( const void *a, const void *b )
|
|
{
|
|
const QuadSortPoint *p0 = (const QuadSortPoint*)a;
|
|
const QuadSortPoint *p1 = (const QuadSortPoint*)b;
|
|
|
|
F32 diff = p1->theta - p0->theta;
|
|
|
|
if ( diff > 0.0f )
|
|
return -1;
|
|
else if ( diff < 0.0f )
|
|
return 1;
|
|
else
|
|
return 0;
|
|
}
|
|
|
|
// Used by sortQuadWindingOrder.
|
|
S32 QSORT_CALLBACK cmpAngleDescending( const void *a, const void *b )
|
|
{
|
|
const QuadSortPoint *p0 = (const QuadSortPoint*)a;
|
|
const QuadSortPoint *p1 = (const QuadSortPoint*)b;
|
|
|
|
F32 diff = p1->theta - p0->theta;
|
|
|
|
if ( diff > 0.0f )
|
|
return 1;
|
|
else if ( diff < 0.0f )
|
|
return -1;
|
|
else
|
|
return 0;
|
|
}
|
|
|
|
void sortQuadWindingOrder( const MatrixF &quadMat, bool clockwise, const Point3F *verts, U32 *vertMap, U32 count )
|
|
{
|
|
PROFILE_SCOPE( MathUtils_sortQuadWindingOrder );
|
|
|
|
if ( count == 0 )
|
|
return;
|
|
|
|
Point3F *quadPoints = new Point3F[count];
|
|
|
|
for ( S32 i = 0; i < count; i++ )
|
|
{
|
|
quadMat.mulP( verts[i], &quadPoints[i] );
|
|
quadPoints[i].normalizeSafe();
|
|
}
|
|
|
|
sortQuadWindingOrder( clockwise, quadPoints, vertMap, count );
|
|
|
|
delete [] quadPoints;
|
|
}
|
|
|
|
void sortQuadWindingOrder( bool clockwise, const Point3F *verts, U32 *vertMap, U32 count )
|
|
{
|
|
QuadSortPoint *sortPoints = new QuadSortPoint[count];
|
|
|
|
for ( S32 i = 0; i < count; i++ )
|
|
{
|
|
QuadSortPoint &sortPnt = sortPoints[i];
|
|
const Point3F &vec = verts[i];
|
|
|
|
sortPnt.id = i;
|
|
|
|
F32 theta = mAtan2( vec.y, vec.x );
|
|
|
|
if ( vec.y < 0.0f )
|
|
theta = M_2PI_F + theta;
|
|
|
|
sortPnt.theta = theta;
|
|
}
|
|
|
|
dQsort( sortPoints, count, sizeof( QuadSortPoint ), clockwise ? cmpAngleDescending : cmpAngleAscending );
|
|
|
|
for ( S32 i = 0; i < count; i++ )
|
|
vertMap[i] = sortPoints[i].id;
|
|
|
|
delete [] sortPoints;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void buildMatrix( const VectorF *rvec, const VectorF *fvec, const VectorF *uvec, const VectorF *pos, MatrixF *outMat )
|
|
{
|
|
/// Work in Progress
|
|
|
|
/*
|
|
AssertFatal( !rvec || rvec->isUnitLength(), "MathUtils::buildMatrix() - Right vector was not normalized!" );
|
|
AssertFatal( !fvec || fvec->isUnitLength(), "MathUtils::buildMatrix() - Forward vector was not normalized!" );
|
|
AssertFatal( !uvec || uvec->isUnitLength(), "MathUtils::buildMatrix() - Up vector was not normalized!" );
|
|
|
|
// Note this relationship:
|
|
//
|
|
// Column0 Column1 Column2
|
|
// Axis X Axis Y Axis Z
|
|
// Rvec Fvec Uvec
|
|
//
|
|
|
|
enum
|
|
{
|
|
RVEC = 1,
|
|
FVEC = 1 << 1,
|
|
UVEC = 1 << 2,
|
|
ALL = RVEC | FVEC | UVEC
|
|
};
|
|
|
|
U8 mask = 0;
|
|
U8 count = 0;
|
|
U8 axis0, axis1;
|
|
|
|
if ( rvec )
|
|
{
|
|
mask |= RVEC;
|
|
axis0 == 0;
|
|
count++;
|
|
}
|
|
if ( fvec )
|
|
{
|
|
mask |= FVEC;
|
|
if ( count == 0 )
|
|
axis0 = 1;
|
|
else
|
|
axis1 = 1;
|
|
count++;
|
|
}
|
|
if ( uvec )
|
|
{
|
|
mask |= UVEC;
|
|
count++;
|
|
}
|
|
|
|
U8 bR = 1;
|
|
U8 bF = 1 << 1;
|
|
U8 bU = 1 << 2;
|
|
U8 bRF = bR | bF;
|
|
U8 bRU = bR | bU;
|
|
U8 bFU = bF | bU;
|
|
U8 bRFU = bR | bF | bU;
|
|
|
|
|
|
|
|
// Cross product map.
|
|
U8 cpdMap[3][2] =
|
|
{
|
|
{ 1, 2 },
|
|
{ 2, 0 },
|
|
{ 0, 1 },
|
|
}
|
|
|
|
if ( count == 1 )
|
|
{
|
|
if ( mask == bR )
|
|
{
|
|
|
|
}
|
|
else if ( mask == bF )
|
|
{
|
|
|
|
}
|
|
else if ( mask == bU )
|
|
{
|
|
|
|
}
|
|
}
|
|
else if ( count == 2 )
|
|
{
|
|
if ( mask == bRF )
|
|
{
|
|
|
|
}
|
|
else if ( mask == bRU )
|
|
{
|
|
|
|
}
|
|
else if ( mask == bFU )
|
|
{
|
|
|
|
}
|
|
}
|
|
else // bRFU
|
|
{
|
|
|
|
}
|
|
|
|
if ( rvec )
|
|
{
|
|
outMat->setColumn( 0, *rvec );
|
|
|
|
if ( fvec )
|
|
{
|
|
outMat->setColumn( 1, *fvec );
|
|
|
|
if ( uvec )
|
|
outMat->setColumn( 2, *uvec );
|
|
else
|
|
{
|
|
// Set uvec from rvec/fvec
|
|
tmp = mCross( rvec, fvec );
|
|
tmp.normalizeSafe();
|
|
outMat->setColumn( 2, tmp );
|
|
}
|
|
}
|
|
else if ( uvec )
|
|
{
|
|
// Set fvec from uvec/rvec
|
|
tmp = mCross( uvec, rvec );
|
|
tmp.normalizeSafe();
|
|
outMat->setColumn( 1, tmp );
|
|
}
|
|
else
|
|
{
|
|
// Set fvec and uvec from rvec
|
|
Point3F tempFvec = mPerp( rvec );
|
|
Point3F tempUvec = mCross( )
|
|
|
|
}
|
|
}
|
|
AssertFatal( rvec->isUnitLength(), "MathUtils::buildMatrix() - Right vector was not normalized!" );
|
|
AssertFatal( fvec->isUnitLength(), "MathUtils::buildMatrix() - Forward vector was not normalized!" );
|
|
AssertFatal( uvec->isUnitLength(), "MathUtils::buildMatrix() - UpVector vector was not normalized!" );
|
|
AssertFatal( outMat, "MathUtils::buildMatrix() - Got null output matrix!" );
|
|
AssertFatal( outMat->isAffine(), "MathUtils::buildMatrix() - Got uninitialized matrix!" );
|
|
*/
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool reduceFrustum( const Frustum& frustum, const RectI& viewport, const RectF& area, Frustum& outFrustum )
|
|
{
|
|
// Just to be safe, clamp the area to the viewport.
|
|
|
|
Point2F clampedMin;
|
|
Point2F clampedMax;
|
|
|
|
clampedMin.x = mClampF( area.extent.x, ( F32 ) viewport.point.x, ( F32 ) viewport.point.x + viewport.extent.x );
|
|
clampedMin.y = mClampF( area.extent.y, ( F32 ) viewport.point.y, ( F32 ) viewport.point.y + viewport.extent.y );
|
|
|
|
clampedMax.x = mClampF( area.extent.x, ( F32 ) viewport.point.x, ( F32 ) viewport.point.x + viewport.extent.x );
|
|
clampedMax.y = mClampF( area.extent.y, ( F32 ) viewport.point.y, ( F32 ) viewport.point.y + viewport.extent.y );
|
|
|
|
// If we have ended up without a visible region on the screen,
|
|
// terminate now.
|
|
|
|
if( mFloor( clampedMin.x ) == mFloor( clampedMax.x ) ||
|
|
mFloor( clampedMin.y ) == mFloor( clampedMax.y ) )
|
|
return false;
|
|
|
|
// Get the extents of the frustum.
|
|
|
|
const F32 frustumXExtent = mFabs( frustum.getNearRight() - frustum.getNearLeft() );
|
|
const F32 frustumYExtent = mFabs( frustum.getNearTop() - frustum.getNearBottom() );
|
|
|
|
// Now, normalize the screen-space pixel coordinates to lie within the screen-centered
|
|
// -1 to 1 coordinate space that is used for the frustum planes.
|
|
|
|
Point2F normalizedMin;
|
|
Point2F normalizedMax;
|
|
|
|
normalizedMin.x = ( ( clampedMin.x / viewport.extent.x ) * frustumXExtent ) - ( frustumXExtent / 2.f );
|
|
normalizedMin.y = ( ( clampedMin.y / viewport.extent.y ) * frustumYExtent ) - ( frustumYExtent / 2.f );
|
|
normalizedMax.x = ( ( clampedMax.x / viewport.extent.x ) * frustumXExtent ) - ( frustumXExtent / 2.f );
|
|
normalizedMax.y = ( ( clampedMax.y / viewport.extent.y ) * frustumYExtent ) - ( frustumYExtent / 2.f );
|
|
|
|
// Make sure the generated frustum metrics are somewhat sane.
|
|
|
|
if( normalizedMax.x - normalizedMin.x < 0.001f ||
|
|
normalizedMax.y - normalizedMin.y < 0.001f )
|
|
return false;
|
|
|
|
// Finally, create the new frustum using the original's frustum
|
|
// information except its left/right/top/bottom planes.
|
|
//
|
|
// Note that screen-space coordinates go upside down on Y whereas
|
|
// camera-space frustum coordinates go downside up on Y which is
|
|
// why we are inverting Y here.
|
|
|
|
outFrustum.set(
|
|
frustum.isOrtho(),
|
|
normalizedMin.x,
|
|
normalizedMax.x,
|
|
- normalizedMin.y,
|
|
- normalizedMax.y,
|
|
frustum.getNearDist(),
|
|
frustum.getFarDist(),
|
|
frustum.getTransform()
|
|
);
|
|
|
|
return true;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void makeFrustum( F32 *outLeft,
|
|
F32 *outRight,
|
|
F32 *outTop,
|
|
F32 *outBottom,
|
|
F32 fovYInRadians,
|
|
F32 aspectRatio,
|
|
F32 nearPlane )
|
|
{
|
|
F32 top = nearPlane * mTan( fovYInRadians / 2.0 );
|
|
if ( outTop ) *outTop = top;
|
|
if ( outBottom ) *outBottom = -top;
|
|
|
|
F32 left = top * aspectRatio;
|
|
if ( outLeft ) *outLeft = -left;
|
|
if ( outRight ) *outRight = left;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void makeProjection( MatrixF *outMatrix,
|
|
F32 fovYInRadians,
|
|
F32 aspectRatio,
|
|
F32 nearPlane,
|
|
F32 farPlane,
|
|
bool gfxRotate )
|
|
{
|
|
F32 left, right, top, bottom;
|
|
makeFrustum( &left, &right, &top, &bottom, fovYInRadians, aspectRatio, nearPlane );
|
|
makeProjection( outMatrix, left, right, top, bottom, nearPlane, farPlane, gfxRotate );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void makeFovPortFrustum(
|
|
Frustum *outFrustum,
|
|
bool isOrtho,
|
|
F32 nearDist,
|
|
F32 farDist,
|
|
const FovPort &inPort,
|
|
const MatrixF &transform)
|
|
{
|
|
F32 leftSize = nearDist * inPort.leftTan;
|
|
F32 rightSize = nearDist * inPort.rightTan;
|
|
F32 upSize = nearDist * inPort.upTan;
|
|
F32 downSize = nearDist * inPort.downTan;
|
|
|
|
F32 left = -leftSize;
|
|
F32 right = rightSize;
|
|
F32 top = upSize;
|
|
F32 bottom = -downSize;
|
|
|
|
outFrustum->set(isOrtho, left, right, top, bottom, nearDist, farDist, transform);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
/// This is the special rotation matrix applied to
|
|
/// projection matricies for GFX.
|
|
///
|
|
/// It is a wart of the OGL to DX change over.
|
|
///
|
|
static const MatrixF sGFXProjRotMatrix( EulerF( (M_PI_F / 2.0f), 0.0f, 0.0f ) );
|
|
|
|
void makeProjection( MatrixF *outMatrix,
|
|
F32 left,
|
|
F32 right,
|
|
F32 top,
|
|
F32 bottom,
|
|
F32 nearPlane,
|
|
F32 farPlane,
|
|
bool gfxRotate )
|
|
{
|
|
Point4F row;
|
|
row.x = 2.0*nearPlane / (right-left);
|
|
row.y = 0.0;
|
|
row.z = 0.0;
|
|
row.w = 0.0;
|
|
outMatrix->setRow( 0, row );
|
|
|
|
row.x = 0.0;
|
|
row.y = 2.0 * nearPlane / (top-bottom);
|
|
row.z = 0.0;
|
|
row.w = 0.0;
|
|
outMatrix->setRow( 1, row );
|
|
|
|
row.x = (left+right) / (right-left);
|
|
row.y = (top+bottom) / (top-bottom);
|
|
row.z = farPlane / (nearPlane - farPlane);
|
|
row.w = -1.0;
|
|
outMatrix->setRow( 2, row );
|
|
|
|
row.x = 0.0;
|
|
row.y = 0.0;
|
|
row.z = nearPlane * farPlane / (nearPlane - farPlane);
|
|
row.w = 0.0;
|
|
outMatrix->setRow( 3, row );
|
|
|
|
outMatrix->transpose();
|
|
|
|
if ( gfxRotate )
|
|
outMatrix->mul( sGFXProjRotMatrix );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void makeOrthoProjection( MatrixF *outMatrix,
|
|
F32 left,
|
|
F32 right,
|
|
F32 top,
|
|
F32 bottom,
|
|
F32 nearPlane,
|
|
F32 farPlane,
|
|
bool gfxRotate )
|
|
{
|
|
Point4F row;
|
|
row.x = 2.0f / (right - left);
|
|
row.y = 0.0f;
|
|
row.z = 0.0f;
|
|
row.w = 0.0f;
|
|
outMatrix->setRow( 0, row );
|
|
|
|
row.x = 0.0f;
|
|
row.y = 2.0f / (top - bottom);
|
|
row.z = 0.0f;
|
|
row.w = 0.0f;
|
|
outMatrix->setRow( 1, row );
|
|
|
|
row.x = 0.0f;
|
|
row.y = 0.0f;
|
|
row.w = 0.0f;
|
|
|
|
//Unlike D3D, which has a 0-1 range, OpenGL uses a -1-1 range.
|
|
//However, epoxy internally handles the swap, so the math here is the same for both APIs
|
|
row.z = 1.0f / (nearPlane - farPlane);
|
|
|
|
outMatrix->setRow( 2, row );
|
|
|
|
row.x = (left + right) / (left - right);
|
|
row.y = (top + bottom) / (bottom - top);
|
|
row.z = nearPlane / (nearPlane - farPlane);
|
|
row.w = 1.0f;
|
|
outMatrix->setRow( 3, row );
|
|
|
|
outMatrix->transpose();
|
|
|
|
if ( gfxRotate )
|
|
outMatrix->mul( sGFXProjRotMatrix );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool edgeFaceIntersect( const Point3F &edgeA, const Point3F &edgeB,
|
|
const Point3F &faceA, const Point3F &faceB, const Point3F &faceC, const Point3F &faceD, Point3F *intersection )
|
|
{
|
|
VectorF edgeAB = edgeB - edgeA;
|
|
VectorF edgeAFaceA = faceA - edgeA;
|
|
VectorF edgeAFaceB = faceB - edgeA;
|
|
VectorF edgeAFaceC = faceC - edgeA;
|
|
|
|
VectorF m = mCross( edgeAFaceC, edgeAB );
|
|
F32 v = mDot( edgeAFaceA, m );
|
|
if ( v >= 0.0f )
|
|
{
|
|
F32 u = -mDot( edgeAFaceB, m );
|
|
if ( u < 0.0f )
|
|
return false;
|
|
|
|
VectorF tmp = mCross( edgeAFaceB, edgeAB );
|
|
F32 w = mDot( edgeAFaceA, tmp );
|
|
if ( w < 0.0f )
|
|
return false;
|
|
|
|
F32 denom = 1.0f / (u + v + w );
|
|
u *= denom;
|
|
v *= denom;
|
|
w *= denom;
|
|
|
|
(*intersection) = u * faceA + v * faceB + w * faceC;
|
|
}
|
|
else
|
|
{
|
|
VectorF edgeAFaceD = faceD - edgeA;
|
|
F32 u = mDot( edgeAFaceD, m );
|
|
if ( u < 0.0f )
|
|
return false;
|
|
|
|
VectorF tmp = mCross( edgeAFaceA, edgeAB );
|
|
F32 w = mDot( edgeAFaceD, tmp );
|
|
if ( w < 0.0f )
|
|
return false;
|
|
|
|
v = -v;
|
|
|
|
F32 denom = 1.0f / ( u + v + w );
|
|
u *= denom;
|
|
v *= denom;
|
|
w *= denom;
|
|
|
|
(*intersection) = u * faceA + v * faceD + w * faceC;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool isPlanarPolygon( const Point3F* vertices, U32 numVertices )
|
|
{
|
|
AssertFatal( vertices != NULL, "MathUtils::isPlanarPolygon - Received NULL pointer" );
|
|
AssertFatal( numVertices >= 3, "MathUtils::isPlanarPolygon - Must have at least three vertices" );
|
|
|
|
// Triangles are always planar. Letting smaller numVertices
|
|
// slip through provides robustness for errors in release builds.
|
|
|
|
if( numVertices <= 3 )
|
|
return true;
|
|
|
|
// Compute the normal of the first triangle in the polygon.
|
|
|
|
Point3F triangle1Normal = mTriangleNormal( vertices[ 0 ], vertices[ 1 ], vertices[ 2 ] );
|
|
|
|
// Now go through all the remaining vertices and build triangles
|
|
// with the first two vertices. Then the normals of all these triangles
|
|
// must be the same (minus some variance due to floating-point inaccuracies)
|
|
// as the normal of the first triangle.
|
|
|
|
for( U32 i = 3; i < numVertices; ++ i )
|
|
{
|
|
Point3F triangle2Normal = mTriangleNormal( vertices[ 0 ], vertices[ 1 ], vertices[ i ] );
|
|
if( !triangle1Normal.equal( triangle2Normal ) )
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool isConvexPolygon( const Point3F* vertices, U32 numVertices )
|
|
{
|
|
AssertFatal( vertices != NULL, "MathUtils::isConvexPolygon - Received NULL pointer" );
|
|
AssertFatal( numVertices >= 3, "MathUtils::isConvexPolygon - Must have at least three vertices" );
|
|
|
|
// Triangles are always convex. Letting smaller numVertices
|
|
// slip through provides robustness for errors in release builds.
|
|
|
|
if( numVertices <= 3 )
|
|
return true;
|
|
|
|
U32 numPositive = 0;
|
|
U32 numNegative = 0;
|
|
|
|
for( U32 i = 0; i < numVertices; ++ i )
|
|
{
|
|
const Point3F& a = vertices[ i ];
|
|
const Point3F& b = vertices[ ( i + 1 ) % numVertices ];
|
|
const Point3F& c = vertices[ ( i + 2 ) % numVertices ];
|
|
|
|
const F32 crossProductLength = mCross( b - a, c - b ).len();
|
|
|
|
if( crossProductLength < 0.f )
|
|
numNegative ++;
|
|
else if( crossProductLength > 0.f )
|
|
numPositive ++;
|
|
|
|
if( numNegative && numPositive )
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
bool clipFrustumByPolygon( const Point3F* points, U32 numPoints, const RectI& viewport, const MatrixF& world,
|
|
const MatrixF& projection, const Frustum& inFrustum, const Frustum& rootFrustum, Frustum& outFrustum )
|
|
{
|
|
enum
|
|
{
|
|
MAX_RESULT_VERTICES = 64,
|
|
MAX_INPUT_VERTICES = MAX_RESULT_VERTICES - Frustum::PlaneCount // Clipping against each plane may add a vertex.
|
|
};
|
|
|
|
AssertFatal( numPoints <= MAX_INPUT_VERTICES, "MathUtils::clipFrustumByPolygon - Too many vertices!" );
|
|
if( numPoints > MAX_INPUT_VERTICES )
|
|
return false;
|
|
|
|
// First, we need to clip the polygon against inFrustum.
|
|
//
|
|
// Use two buffers here in interchanging roles as sources and targets
|
|
// in clipping against the frustum planes.
|
|
|
|
Point3F polygonBuffer1[ MAX_RESULT_VERTICES ];
|
|
Point3F polygonBuffer2[ MAX_RESULT_VERTICES ];
|
|
|
|
Point3F* tempPolygon = polygonBuffer1;
|
|
Point3F* clippedPolygon = polygonBuffer2;
|
|
|
|
dMemcpy( clippedPolygon, points, numPoints * sizeof( points[ 0 ] ) );
|
|
|
|
U32 numClippedPolygonVertices = numPoints;
|
|
U32 numTempPolygonVertices = 0;
|
|
|
|
for( U32 nplane = 0; nplane < Frustum::PlaneCount; ++ nplane )
|
|
{
|
|
// Make the output of the last iteration the
|
|
// input of this iteration.
|
|
|
|
swap( tempPolygon, clippedPolygon );
|
|
numTempPolygonVertices = numClippedPolygonVertices;
|
|
|
|
// Clip our current remainder of the original polygon
|
|
// against the current plane.
|
|
|
|
const PlaneF& plane = inFrustum.getPlanes()[ nplane ];
|
|
numClippedPolygonVertices = plane.clipPolygon( tempPolygon, numTempPolygonVertices, clippedPolygon );
|
|
|
|
// If the polygon was completely on the backside of the plane,
|
|
// then polygon is outside the frustum. In this case, return false
|
|
// to indicate we haven't clipped anything.
|
|
|
|
if( !numClippedPolygonVertices )
|
|
return false;
|
|
}
|
|
|
|
// Project the clipped polygon into screen space.
|
|
|
|
MatrixF worldProjection = projection;
|
|
worldProjection.mul( world ); // Premultiply world*projection so we don't have to do this over and over for each point.
|
|
|
|
Point3F projectedPolygon[ 10 ];
|
|
for( U32 i = 0; i < numClippedPolygonVertices; ++ i )
|
|
mProjectWorldToScreen(
|
|
clippedPolygon[ i ],
|
|
&projectedPolygon[ i ],
|
|
viewport,
|
|
worldProjection
|
|
);
|
|
|
|
// Put an axis-aligned rectangle around our polygon.
|
|
|
|
Point2F minPoint( projectedPolygon[ 0 ].x, projectedPolygon[ 0 ].y );
|
|
Point2F maxPoint( projectedPolygon[ 0 ].x, projectedPolygon[ 0 ].y );
|
|
|
|
for( U32 i = 1; i < numClippedPolygonVertices; ++ i )
|
|
{
|
|
minPoint.setMin( Point2F( projectedPolygon[ i ].x, projectedPolygon[ i ].y ) );
|
|
maxPoint.setMax( Point2F( projectedPolygon[ i ].x, projectedPolygon[ i ].y ) );
|
|
}
|
|
|
|
RectF area( minPoint, maxPoint - minPoint );
|
|
|
|
// Finally, reduce the input frustum to the given area. Note that we
|
|
// use rootFrustum here instead of inFrustum as the latter does not necessarily
|
|
// represent the full viewport we are using here which thus would skew the mapping.
|
|
|
|
return reduceFrustum( rootFrustum, viewport, area, outFrustum );
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
U32 extrudePolygonEdges( const Point3F* vertices, U32 numVertices, const Point3F& direction, PlaneF* outPlanes )
|
|
{
|
|
U32 numPlanes = 0;
|
|
U32 lastVertex = numVertices - 1;
|
|
bool invert = false;
|
|
|
|
for( U32 i = 0; i < numVertices; lastVertex = i, ++ i )
|
|
{
|
|
const Point3F& v1 = vertices[ i ];
|
|
const Point3F& v2 = vertices[ lastVertex ];
|
|
|
|
// Skip the edge if it's length is really short.
|
|
|
|
const Point3F edgeVector = v2 - v1;
|
|
if( edgeVector.len() < 0.05 )
|
|
continue;
|
|
|
|
// Compute the plane normal. The direction and the edge vector
|
|
// basically define the orientation of the plane so their cross
|
|
// product is the plane normal.
|
|
|
|
Point3F normal;
|
|
if( !invert )
|
|
normal = mCross( edgeVector, direction );
|
|
else
|
|
normal = mCross( direction, edgeVector );
|
|
|
|
// Create a plane for the edge.
|
|
|
|
outPlanes[ numPlanes ] = PlaneF( v1, normal );
|
|
numPlanes ++;
|
|
|
|
// If this is the first plane that we have created, find out whether
|
|
// the vertex ordering is giving us the plane orientations that we want
|
|
// (facing inside). If not, invert vertex order from now on.
|
|
|
|
if( i == 0 )
|
|
{
|
|
const PlaneF& plane = outPlanes[ numPlanes - 1 ];
|
|
for( U32 n = i + 1; n < numVertices; ++ n )
|
|
{
|
|
const PlaneF::Side side = plane.whichSide( vertices[ n ] );
|
|
if( side == PlaneF::On )
|
|
continue;
|
|
|
|
if( side != PlaneF::Front )
|
|
invert = true;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
return numPlanes;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
U32 extrudePolygonEdgesFromPoint( const Point3F* vertices, U32 numVertices, const Point3F& fromPoint, PlaneF* outPlanes )
|
|
{
|
|
U32 numPlanes = 0;
|
|
U32 lastVertex = numVertices - 1;
|
|
bool invert = false;
|
|
|
|
for( U32 i = 0; i < numVertices; lastVertex = i, ++ i )
|
|
{
|
|
const Point3F& v1 = vertices[ i ];
|
|
const Point3F& v2 = vertices[ lastVertex ];
|
|
|
|
// Skip the edge if it's length is really short.
|
|
|
|
const Point3F edgeVector = v2 - v1;
|
|
if( edgeVector.len() < 0.05 )
|
|
continue;
|
|
|
|
// Create a plane for the edge.
|
|
|
|
if( !invert )
|
|
outPlanes[ numPlanes ] = PlaneF( v1, fromPoint, v2 );
|
|
else
|
|
outPlanes[ numPlanes ] = PlaneF( v2, fromPoint, v1 );
|
|
|
|
numPlanes ++;
|
|
|
|
// If this is the first plane that we have created, find out whether
|
|
// the vertex ordering is giving us the plane orientations that we want
|
|
// (facing inside). If not, invert vertex order from now on.
|
|
|
|
if( i == 0 )
|
|
{
|
|
const PlaneF& plane = outPlanes[ numPlanes - 1 ];
|
|
for( U32 n = i + 1; n < numVertices; ++ n )
|
|
{
|
|
const PlaneF::Side side = plane.whichSide( vertices[ n ] );
|
|
if( side == PlaneF::On )
|
|
continue;
|
|
|
|
if( side != PlaneF::Front )
|
|
invert = true;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
return numPlanes;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void mBuildHull2D(const Vector<Point2F> _inPoints, Vector<Point2F> &hullPoints)
|
|
{
|
|
/// Andrew's monotone chain convex hull algorithm implementation
|
|
|
|
struct Util
|
|
{
|
|
//compare by x and then by y
|
|
static int CompareLexicographic( const Point2F *a, const Point2F *b)
|
|
{
|
|
return a->x < b->x || (a->x == b->x && a->y < b->y);
|
|
}
|
|
};
|
|
|
|
hullPoints.clear();
|
|
hullPoints.setSize( _inPoints.size()*2 );
|
|
|
|
// sort in points by x and then by y
|
|
Vector<Point2F> inSortedPoints = _inPoints;
|
|
inSortedPoints.sort( &Util::CompareLexicographic );
|
|
|
|
Point2F* lowerHullPtr = hullPoints.address();
|
|
U32 lowerHullIdx = 0;
|
|
|
|
//lower part of hull
|
|
for( int i = 0; i < inSortedPoints.size(); ++i )
|
|
{
|
|
while( lowerHullIdx >= 2 && mCross( lowerHullPtr[ lowerHullIdx - 2], lowerHullPtr[lowerHullIdx - 1], inSortedPoints[i] ) <= 0 )
|
|
--lowerHullIdx;
|
|
|
|
lowerHullPtr[lowerHullIdx++] = inSortedPoints[i];
|
|
}
|
|
|
|
--lowerHullIdx; // last point are the same as first in upperHullPtr
|
|
|
|
Point2F* upperHullPtr = hullPoints.address() + lowerHullIdx;
|
|
U32 upperHullIdx = 0;
|
|
|
|
//upper part of hull
|
|
for( int i = inSortedPoints.size()-1; i >= 0; --i )
|
|
{
|
|
while( upperHullIdx >= 2 && mCross( upperHullPtr[ upperHullIdx - 2], upperHullPtr[upperHullIdx - 1], inSortedPoints[i] ) <= 0 )
|
|
--upperHullIdx;
|
|
|
|
upperHullPtr[upperHullIdx++] = inSortedPoints[i];
|
|
}
|
|
|
|
hullPoints.setSize( lowerHullIdx + upperHullIdx );
|
|
}
|
|
|
|
} // namespace MathUtils
|