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Documentation                       Search   bezier_patch.cpp Go to the documentation of this file. /* Copyright, 2000 Nevrax Ltd. * * This file is part of NEVRAX NEL. * NEVRAX NEL is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2, or (at your option) * any later version. * NEVRAX NEL is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * You should have received a copy of the GNU General Public License * along with NEVRAX NEL; see the file COPYING. If not, write to the * Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, * MA 02111-1307, USA. */ #include "std3d.h" #include "3d/bezier_patch.h" using namespace NLMISC; namespace NL3D { // *************************************************************************** void CBezierPatch::make(CVector vertices[4], CVector normals[4]) { sint i; static sint starts[8]= {0,1, 1,2, 2,3, 3,0}; static sint ends[8]= {1,0, 2,1, 3,2, 0,3}; for(i=0;i<4;i++) Vertices[i]= vertices[i]; // For all tangents. for(i=0;i<8;i++) { CVector tgt= Vertices[ends[i]] - Vertices[starts[i]]; CVector I,J,K; J= normals[starts[i]]; I= J^tgt; K= I^J; K.normalize(); // Yes, we store tangents as position, not vectors... Tangents[i]= Vertices[starts[i]] + K*tgt.norm()/3; } makeInteriors(); } // *************************************************************************** void CBezierPatch::makeInteriors() { CVector &a = Vertices[0]; CVector &b = Vertices[1]; CVector &c = Vertices[2]; CVector &d = Vertices[3]; Interiors[0] = Tangents[7] + Tangents[0] - a; Interiors[1] = Tangents[1] + Tangents[2] - b; Interiors[2] = Tangents[3] + Tangents[4] - c; Interiors[3] = Tangents[5] + Tangents[6] - d; } // *************************************************************************** void CBezierPatch::applyMatrix(const CMatrix &m) { sint i; for(i=0;i<4;i++) Vertices[i]= m*Vertices[i]; for(i=0;i<8;i++) Tangents[i]= m*Tangents[i]; for(i=0;i<4;i++) Interiors[i]= m*Interiors[i]; } // *************************************************************************** static inline void mulAdd(CVector &tgt, const CVector &src, float f) { tgt.x+= src.x*f; tgt.y+= src.y*f; tgt.z+= src.z*f; } // *************************************************************************** static inline void mulAddD(CVectorD &tgt, const CVector &src, double f) { tgt.x+= src.x*f; tgt.y+= src.y*f; tgt.z+= src.z*f; } // *************************************************************************** CVector CBezierPatch::eval(float ps, float pt) const { CVector p; float ps2 = ps * ps; float ps1 = 1.0f - ps; float ps12 = ps1 * ps1; float s0 = ps12 * ps1; float s1 = 3.0f * ps * ps12; float s2 = 3.0f * ps2 * ps1; float s3 = ps2 * ps; float pt2 = pt * pt; float pt1 = 1.0f - pt; float pt12 = pt1 * pt1; float t0 = pt12 * pt1; float t1 = 3.0f * pt * pt12; float t2 = 3.0f * pt2 * pt1; float t3 = pt2 * pt; p.set(0,0,0); mulAdd(p, Vertices[0] , s0 * t0); mulAdd(p, Tangents[7] , s1 * t0); mulAdd(p, Tangents[6] , s2 * t0); mulAdd(p, Vertices[3] , s3 * t0); mulAdd(p, Tangents[0] , s0 * t1); mulAdd(p, Interiors[0], s1 * t1); mulAdd(p, Interiors[3], s2 * t1); mulAdd(p, Tangents[5] , s3 * t1); mulAdd(p, Tangents[1] , s0 * t2); mulAdd(p, Interiors[1], s1 * t2); mulAdd(p, Interiors[2], s2 * t2); mulAdd(p, Tangents[4] , s3 * t2); mulAdd(p, Vertices[1] , s0 * t3); mulAdd(p, Tangents[2] , s1 * t3); mulAdd(p, Tangents[3] , s2 * t3); mulAdd(p, Vertices[2] , s3 * t3); return p; } // *************************************************************************** CVectorD CBezierPatch::evalDouble(double ps, double pt) const { CVectorD p; double ps2 = ps * ps; double ps1 = 1.0f - ps; double ps12 = ps1 * ps1; double s0 = ps12 * ps1; double s1 = 3.0f * ps * ps12; double s2 = 3.0f * ps2 * ps1; double s3 = ps2 * ps; double pt2 = pt * pt; double pt1 = 1.0f - pt; double pt12 = pt1 * pt1; double t0 = pt12 * pt1; double t1 = 3.0f * pt * pt12; double t2 = 3.0f * pt2 * pt1; double t3 = pt2 * pt; p.set(0,0,0); mulAddD(p, Vertices[0] , s0 * t0); mulAddD(p, Tangents[7] , s1 * t0); mulAddD(p, Tangents[6] , s2 * t0); mulAddD(p, Vertices[3] , s3 * t0); mulAddD(p, Tangents[0] , s0 * t1); mulAddD(p, Interiors[0], s1 * t1); mulAddD(p, Interiors[3], s2 * t1); mulAddD(p, Tangents[5] , s3 * t1); mulAddD(p, Tangents[1] , s0 * t2); mulAddD(p, Interiors[1], s1 * t2); mulAddD(p, Interiors[2], s2 * t2); mulAddD(p, Tangents[4] , s3 * t2); mulAddD(p, Vertices[1] , s0 * t3); mulAddD(p, Tangents[2] , s1 * t3); mulAddD(p, Tangents[3] , s2 * t3); mulAddD(p, Vertices[2] , s3 * t3); return p; } // *************************************************************************** CVector CBezierPatch::evalNormal(float ps, float pt) const { CVector tgtS, tgtT; float s0,s1,s2,s3; float t0,t1,t2,t3; float ps2 = ps * ps; float ps1 = 1.0f - ps; float ps12 = ps1 * ps1; float pt2 = pt * pt; float pt1 = 1.0f - pt; float pt12 = pt1 * pt1; // Compute tangentS //================= // s/ds. s0 = -3* ps12; s1 = 9*ps2 + 3 -12*ps; s2 =-9*ps2 + 6*ps ; s3 = 3* ps2; // t/dt. t0 = pt12 * pt1; t1 = 3.0f * pt * pt12; t2 = 3.0f * pt2 * pt1; t3 = pt2 * pt; tgtS.set(0,0,0); mulAdd(tgtS, Vertices[0] , s0 * t0); mulAdd(tgtS, Tangents[7] , s1 * t0); mulAdd(tgtS, Tangents[6] , s2 * t0); mulAdd(tgtS, Vertices[3] , s3 * t0); mulAdd(tgtS, Tangents[0] , s0 * t1); mulAdd(tgtS, Interiors[0], s1 * t1); mulAdd(tgtS, Interiors[3], s2 * t1); mulAdd(tgtS, Tangents[5] , s3 * t1); mulAdd(tgtS, Tangents[1] , s0 * t2); mulAdd(tgtS, Interiors[1], s1 * t2); mulAdd(tgtS, Interiors[2], s2 * t2); mulAdd(tgtS, Tangents[4] , s3 * t2); mulAdd(tgtS, Vertices[1] , s0 * t3); mulAdd(tgtS, Tangents[2] , s1 * t3); mulAdd(tgtS, Tangents[3] , s2 * t3); mulAdd(tgtS, Vertices[2] , s3 * t3); // Compute tangentT //================= // s/ds. s0 = ps12 * ps1; s1 = 3.0f * ps * ps12; s2 = 3.0f * ps2 * ps1; s3 = ps2 * ps; // t/dt. t0 = -3* pt12; t1 = 9*pt2 + 3 -12*pt; t2 =-9*pt2 + 6*pt ; t3 = 3* pt2; tgtT.set(0,0,0); mulAdd(tgtT, Vertices[0] , s0 * t0); mulAdd(tgtT, Tangents[7] , s1 * t0); mulAdd(tgtT, Tangents[6] , s2 * t0); mulAdd(tgtT, Vertices[3] , s3 * t0); mulAdd(tgtT, Tangents[0] , s0 * t1); mulAdd(tgtT, Interiors[0], s1 * t1); mulAdd(tgtT, Interiors[3], s2 * t1); mulAdd(tgtT, Tangents[5] , s3 * t1); mulAdd(tgtT, Tangents[1] , s0 * t2); mulAdd(tgtT, Interiors[1], s1 * t2); mulAdd(tgtT, Interiors[2], s2 * t2); mulAdd(tgtT, Tangents[4] , s3 * t2); mulAdd(tgtT, Vertices[1] , s0 * t3); mulAdd(tgtT, Tangents[2] , s1 * t3); mulAdd(tgtT, Tangents[3] , s2 * t3); mulAdd(tgtT, Vertices[2] , s3 * t3); // Return the normal. CVector norm= tgtT^tgtS; norm.normalize(); return norm; } // *************************************************************************** CVector CBezierPatch::evalTangentS(float ps, float pt) const { CVector tgtS; float s0,s1,s2,s3; float t0,t1,t2,t3; float ps2 = ps * ps; float ps1 = 1.0f - ps; float ps12 = ps1 * ps1; float pt2 = pt * pt; float pt1 = 1.0f - pt; float pt12 = pt1 * pt1; // Compute tangentS //================= // s/ds. s0 = -3* ps12; s1 = 9*ps2 + 3 -12*ps; s2 =-9*ps2 + 6*ps ; s3 = 3* ps2; // t/dt. t0 = pt12 * pt1; t1 = 3.0f * pt * pt12; t2 = 3.0f * pt2 * pt1; t3 = pt2 * pt; tgtS.set(0,0,0); mulAdd(tgtS, Vertices[0] , s0 * t0); mulAdd(tgtS, Tangents[7] , s1 * t0); mulAdd(tgtS, Tangents[6] , s2 * t0); mulAdd(tgtS, Vertices[3] , s3 * t0); mulAdd(tgtS, Tangents[0] , s0 * t1); mulAdd(tgtS, Interiors[0], s1 * t1); mulAdd(tgtS, Interiors[3], s2 * t1); mulAdd(tgtS, Tangents[5] , s3 * t1); mulAdd(tgtS, Tangents[1] , s0 * t2); mulAdd(tgtS, Interiors[1], s1 * t2); mulAdd(tgtS, Interiors[2], s2 * t2); mulAdd(tgtS, Tangents[4] , s3 * t2); mulAdd(tgtS, Vertices[1] , s0 * t3); mulAdd(tgtS, Tangents[2] , s1 * t3); mulAdd(tgtS, Tangents[3] , s2 * t3); mulAdd(tgtS, Vertices[2] , s3 * t3); // Return the tgt normalized return tgtS.normed(); } // *************************************************************************** CVector CBezierPatch::evalTangentT(float ps, float pt) const { CVector tgtT; float s0,s1,s2,s3; float t0,t1,t2,t3; float ps2 = ps * ps; float ps1 = 1.0f - ps; float ps12 = ps1 * ps1; float pt2 = pt * pt; float pt1 = 1.0f - pt; float pt12 = pt1 * pt1; // Compute tangentT //================= // s/ds. s0 = ps12 * ps1; s1 = 3.0f * ps * ps12; s2 = 3.0f * ps2 * ps1; s3 = ps2 * ps; // t/dt. t0 = -3* pt12; t1 = 9*pt2 + 3 -12*pt; t2 =-9*pt2 + 6*pt ; t3 = 3* pt2; tgtT.set(0,0,0); mulAdd(tgtT, Vertices[0] , s0 * t0); mulAdd(tgtT, Tangents[7] , s1 * t0); mulAdd(tgtT, Tangents[6] , s2 * t0); mulAdd(tgtT, Vertices[3] , s3 * t0); mulAdd(tgtT, Tangents[0] , s0 * t1); mulAdd(tgtT, Interiors[0], s1 * t1); mulAdd(tgtT, Interiors[3], s2 * t1); mulAdd(tgtT, Tangents[5] , s3 * t1); mulAdd(tgtT, Tangents[1] , s0 * t2); mulAdd(tgtT, Interiors[1], s1 * t2); mulAdd(tgtT, Interiors[2], s2 * t2); mulAdd(tgtT, Tangents[4] , s3 * t2); mulAdd(tgtT, Vertices[1] , s0 * t3); mulAdd(tgtT, Tangents[2] , s1 * t3); mulAdd(tgtT, Tangents[3] , s2 * t3); mulAdd(tgtT, Vertices[2] , s3 * t3); // Return the tgt normalized return tgtT.normed(); } // *************************************************************************** void CBezierPatch::CBezierCurve::subdivide(CBezierCurve &left, CBezierCurve &right, float t) { float t1= 1-t; // Subdivide the 2 curves. left.P0= P0; right.P3= P3; left.P1= t1*P0 + t*P1; right.P2= t1*P2 + t*P3; CVector middle12= t1*P1 + t*P2; left.P2= t1*left.P1 + t*middle12; right.P1= t1*middle12 + t*right.P2; left.P3= right.P0= t1*left.P2 + t*right.P1; } // *************************************************************************** void CBezierPatch::subdivideS(CBezierPatch &left, CBezierPatch &right, float s) const { CBezierCurve curveT[4]; CBezierCurve curveTLeft[4]; CBezierCurve curveTRight[4]; // Setup horizontal curves. curveT[0].set(Vertices[0], Tangents[7] , Tangents[6] , Vertices[3]); curveT[1].set(Tangents[0], Interiors[0], Interiors[3], Tangents[5]); curveT[2].set(Tangents[1], Interiors[1], Interiors[2], Tangents[4]); curveT[3].set(Vertices[1], Tangents[2] , Tangents[3] , Vertices[2]); // Subdivide curves. for(sint i=0;i<4;i++) curveT[i].subdivide(curveTLeft[i], curveTRight[i], s); // Setup bezier patchs. // left. curveTLeft[0].get(left.Vertices[0], left.Tangents[7] , left.Tangents[6] , left.Vertices[3]); curveTLeft[1].get(left.Tangents[0], left.Interiors[0], left.Interiors[3], left.Tangents[5]); curveTLeft[2].get(left.Tangents[1], left.Interiors[1], left.Interiors[2], left.Tangents[4]); curveTLeft[3].get(left.Vertices[1], left.Tangents[2] , left.Tangents[3] , left.Vertices[2]); // right. curveTRight[0].get(right.Vertices[0], right.Tangents[7] , right.Tangents[6] , right.Vertices[3]); curveTRight[1].get(right.Tangents[0], right.Interiors[0], right.Interiors[3], right.Tangents[5]); curveTRight[2].get(right.Tangents[1], right.Interiors[1], right.Interiors[2], right.Tangents[4]); curveTRight[3].get(right.Vertices[1], right.Tangents[2] , right.Tangents[3] , right.Vertices[2]); } // *************************************************************************** void CBezierPatch::subdivideT(CBezierPatch &top, CBezierPatch &bottom, float t) const { CBezierCurve curveS[4]; CBezierCurve curveSTop[4]; CBezierCurve curveSBottom[4]; // Setup vertical curves. curveS[0].set(Vertices[0], Tangents[0] , Tangents[1] , Vertices[1]); curveS[1].set(Tangents[7], Interiors[0], Interiors[1], Tangents[2]); curveS[2].set(Tangents[6], Interiors[3], Interiors[2], Tangents[3]); curveS[3].set(Vertices[3], Tangents[5] , Tangents[4] , Vertices[2]); // Subdivide curves. for(sint i=0;i<4;i++) curveS[i].subdivide(curveSTop[i], curveSBottom[i], t); // Setup bezier patchs. // top. curveSTop[0].get(top.Vertices[0], top.Tangents[0] , top.Tangents[1] , top.Vertices[1]); curveSTop[1].get(top.Tangents[7], top.Interiors[0], top.Interiors[1], top.Tangents[2]); curveSTop[2].get(top.Tangents[6], top.Interiors[3], top.Interiors[2], top.Tangents[3]); curveSTop[3].get(top.Vertices[3], top.Tangents[5] , top.Tangents[4] , top.Vertices[2]); // bottom. curveSBottom[0].get(bottom.Vertices[0], bottom.Tangents[0] , bottom.Tangents[1] , bottom.Vertices[1]); curveSBottom[1].get(bottom.Tangents[7], bottom.Interiors[0], bottom.Interiors[1], bottom.Tangents[2]); curveSBottom[2].get(bottom.Tangents[6], bottom.Interiors[3], bottom.Interiors[2], bottom.Tangents[3]); curveSBottom[3].get(bottom.Vertices[3], bottom.Tangents[5] , bottom.Tangents[4] , bottom.Vertices[2]); } } // NL3D