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#include "curve.h"
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int Hermite::bends(Real *l, const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
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Real roots[2];
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int count = solve_equation(
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roots,
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p0 + t0 ,
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-6*p0 + 6*p1 - 4*t0 + 2*t1,
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6*p0 - 6*p1 + 3*t0 + 3*t1 );
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int valid_count = 0;
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for(Real *i = roots, *end = i + count; i != end; ++i)
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if (less(0, *i) && less(*i, 1)) {
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if (l) l[valid_count] = *i;
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++valid_count;
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}
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return valid_count;
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}
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Range Hermite::bounds_accurate(const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
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Range range(p0);
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range.expand(p1);
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Real roots[2];
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int count = bends(roots, p0, p1, t0, t1);
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for(Real *i = roots, *end = i + count; i != end; ++i)
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range.expand( p(*i, p0, p1, t0, t1) );
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return range;
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}
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int Hermite::intersections(Real *l, const Real &p, const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
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Real roots[3];
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int count = solve_equation(
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roots,
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p0 - p ,
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t0 ,
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-3*p0 + 3*p1 - 2*t0 - t1,
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2*p0 - 2*p1 + t0 + t1 );
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int valid_count = 0;
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for(Real *i = roots, *end = i + count; i != end; ++i)
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if (less(0, *i) && less(*i, 1)) {
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if (l) l[valid_count] = *i;
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++valid_count;
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}
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return valid_count;
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}
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int Bezier::bends(Real *l, const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
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Real roots[2];
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int count = solve_equation(
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roots,
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-p0 + pp0 ,
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2*p0 - 6*pp0 + 2*pp1 ,
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-p0 + 3*pp0 - 3*pp1 + p1 );
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int valid_count = 0;
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for(Real *i = roots, *end = i + count; i != end; ++i)
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if (less(0, *i) && less(*i, 1)) {
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if (l) l[valid_count] = *i;
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++valid_count;
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}
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return valid_count;
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}
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Range Bezier::bounds_accurate(const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
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Range range(p0);
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range.expand(p1);
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Real roots[2];
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int count = bends(roots, p0, p1, pp0, pp1);
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for(Real *i = roots, *end = i + count; i != end; ++i)
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range.expand( p(*i, p0, p1, pp0, pp1) );
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return range;
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}
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int Bezier::intersections(Real *l, const Real &p, const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
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Real roots[3];
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int count = solve_equation(
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roots,
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p0 - p ,
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-3*p0 + 3*pp0 ,
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3*p0 - 6*pp0 + 3*pp1 ,
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-p0 + 3*pp0 - 3*pp1 + p1 );
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int valid_count = 0;
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for(Real *i = roots, *end = i + count; i != end; ++i)
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if (less(0, *i) && less(*i, 1)) {
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if (l) l[valid_count] = *i;
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++valid_count;
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}
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return valid_count;
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}
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