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Bernstein polynomials with no branching. (#591)

pull/480/merge
phkahler 2020-05-02 14:56:50 -04:00 committed by GitHub
parent 76b3efbd08
commit 7366a6c53d
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2 changed files with 19 additions and 76 deletions
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91
src/srf/ratpoly.cpp
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@ -13,84 +13,31 @@
// and convergence should be fast by now.
#define RATPOLY_EPS (LENGTH_EPS/(1e2))
double SolveSpace::Bernstein(int k, int deg, double t)
static double Bernstein(int k, int deg, double t)
{
if(k > deg || k < 0) return 0;
// indexed by [degree][k][exponent]
static const double bernstein_coeff[4][4][4] = {
{ { 1.0,0.0,0.0,0.0 }, { 1.0,0.0,0.0,0.0 }, { 1.0,0.0,0.0,0.0 }, { 1.0,0.0,0.0,0.0 } },
{ { 1.0,-1.0,0.0,0.0 }, { 0.0,1.0,0.0,0.0 }, { 0.0,0.0,0.0,0.0 }, { 0.0,0.0,0.0,0.0 } },
{ { 1.0,-2.0,1.0,0.0 }, { 0.0,2.0,-2.0,0.0 },{ 0.0,0.0,1.0,0.0 }, { 0.0,0.0,0.0,0.0 } },
{ { 1.0,-3.0,3.0,-1.0 },{ 0.0,3.0,-6.0,3.0 },{ 0.0,0.0,3.0,-3.0}, { 0.0,0.0,0.0,1.0 } } };
switch(deg) {
case 0:
return 1;
case 1:
if(k == 0) {
return (1 - t);
} else if(k == 1) {
return t;
}
break;
case 2:
if(k == 0) {
return (1 - t)*(1 - t);
} else if(k == 1) {
return 2*(1 - t)*t;
} else if(k == 2) {
return t*t;
}
break;
case 3:
if(k == 0) {
return (1 - t)*(1 - t)*(1 - t);
} else if(k == 1) {
return 3*(1 - t)*(1 - t)*t;
} else if(k == 2) {
return 3*(1 - t)*t*t;
} else if(k == 3) {
return t*t*t;
}
break;
}
ssassert(false, "Unexpected degree of spline");
const double *c;
c = bernstein_coeff[deg][k];
return (((c[3]*t+c[2])*t)+c[1])*t+c[0];
}
double SolveSpace::BernsteinDerivative(int k, int deg, double t)
static double BernsteinDerivative(int k, int deg, double t)
{
switch(deg) {
case 0:
return 0;
static const double bernstein_derivative_coeff[4][4][3] = {
{ { 0.0,0.0,0.0 }, { 0.0,0.0,0.0 }, { 0.0,0.0,0.0 }, { 0.0,0.0,0.0 } },
{ { -1.0,0.0,0.0 }, { 1.0,0.0,0.0 }, { 0.0,0.0,0.0 }, { 0.0,0.0,0.0 } },
{ { -2.0,2.0,0.0 }, { 2.0,-4.0,0.0 },{ 0.0,2.0,0.0 }, { 0.0,0.0,0.0 } },
{ { -3.0,6.0,-3.0 },{ 3.0,-12.0,9.0 },{ 0.0,6.0,-9.0}, { 0.0,0.0,3.0 } } };
case 1:
if(k == 0) {
return -1;
} else if(k == 1) {
return 1;
}
break;
case 2:
if(k == 0) {
return -2 + 2*t;
} else if(k == 1) {
return 2 - 4*t;
} else if(k == 2) {
return 2*t;
}
break;
case 3:
if(k == 0) {
return -3 + 6*t - 3*t*t;
} else if(k == 1) {
return 3 - 12*t + 9*t*t;
} else if(k == 2) {
return 6*t - 9*t*t;
} else if(k == 3) {
return 3*t*t;
}
break;
}
ssassert(false, "Unexpected degree of spline");
const double *c;
c = bernstein_derivative_coeff[deg][k];
return ((c[2]*t)+c[1])*t+c[0];
}
Vector SBezier::PointAt(double t) const {

4
src/srf/surface.h
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@ -10,10 +10,6 @@
#ifndef SOLVESPACE_SURFACE_H
#define SOLVESPACE_SURFACE_H
// Utility functions, Bernstein polynomials of order 1-3 and their derivatives.
double Bernstein(int k, int deg, double t);
double BernsteinDerivative(int k, int deg, double t);
class SBezierList;
class SSurface;
class SCurvePt;