--- /dev/null
+/*
+Copyright (C) 2001-2006, William Joseph.
+All Rights Reserved.
+
+This file is part of GtkRadiant.
+
+GtkRadiant 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 of the License, or
+(at your option) any later version.
+
+GtkRadiant 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 GtkRadiant; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+*/
+
+#if !defined(INCLUDED_MATH_CURVE_H)
+#define INCLUDED_MATH_CURVE_H
+
+/// \file
+/// \brief Curve data types and related operations.
+
+#include "debugging/debugging.h"
+#include "container/array.h"
+#include <math/matrix.h>
+
+
+template<typename I, typename Degree>
+struct BernsteinPolynomial
+{
+ static double apply(double t)
+ {
+ return 1; // general case not implemented
+ }
+};
+
+typedef IntegralConstant<0> Zero;
+typedef IntegralConstant<1> One;
+typedef IntegralConstant<2> Two;
+typedef IntegralConstant<3> Three;
+typedef IntegralConstant<4> Four;
+
+template<>
+struct BernsteinPolynomial<Zero, Zero>
+{
+ static double apply(double t)
+ {
+ return 1;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<Zero, One>
+{
+ static double apply(double t)
+ {
+ return 1 - t;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<One, One>
+{
+ static double apply(double t)
+ {
+ return t;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<Zero, Two>
+{
+ static double apply(double t)
+ {
+ return (1 - t) * (1 - t);
+ }
+};
+
+template<>
+struct BernsteinPolynomial<One, Two>
+{
+ static double apply(double t)
+ {
+ return 2 * (1 - t) * t;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<Two, Two>
+{
+ static double apply(double t)
+ {
+ return t * t;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<Zero, Three>
+{
+ static double apply(double t)
+ {
+ return (1 - t) * (1 - t) * (1 - t);
+ }
+};
+
+template<>
+struct BernsteinPolynomial<One, Three>
+{
+ static double apply(double t)
+ {
+ return 3 * (1 - t) * (1 - t) * t;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<Two, Three>
+{
+ static double apply(double t)
+ {
+ return 3 * (1 - t) * t * t;
+ }
+};
+
+template<>
+struct BernsteinPolynomial<Three, Three>
+{
+ static double apply(double t)
+ {
+ return t * t * t;
+ }
+};
+
+typedef Array<Vector3> ControlPoints;
+
+inline Vector3 CubicBezier_evaluate(const Vector3* firstPoint, double t)
+{
+ Vector3 result(0, 0, 0);
+ double denominator = 0;
+
+ {
+ double weight = BernsteinPolynomial<Zero, Three>::apply(t);
+ result += vector3_scaled(*firstPoint++, weight);
+ denominator += weight;
+ }
+ {
+ double weight = BernsteinPolynomial<One, Three>::apply(t);
+ result += vector3_scaled(*firstPoint++, weight);
+ denominator += weight;
+ }
+ {
+ double weight = BernsteinPolynomial<Two, Three>::apply(t);
+ result += vector3_scaled(*firstPoint++, weight);
+ denominator += weight;
+ }
+ {
+ double weight = BernsteinPolynomial<Three, Three>::apply(t);
+ result += vector3_scaled(*firstPoint++, weight);
+ denominator += weight;
+ }
+
+ return result / denominator;
+}
+
+inline Vector3 CubicBezier_evaluateMid(const Vector3* firstPoint)
+{
+ return vector3_scaled(firstPoint[0], 0.125)
+ + vector3_scaled(firstPoint[1], 0.375)
+ + vector3_scaled(firstPoint[2], 0.375)
+ + vector3_scaled(firstPoint[3], 0.125);
+}
+
+inline Vector3 CatmullRom_evaluate(const ControlPoints& controlPoints, double t)
+{
+ // scale t to be segment-relative
+ t *= double(controlPoints.size() - 1);
+
+ // subtract segment index;
+ std::size_t segment = 0;
+ for(std::size_t i = 0; i < controlPoints.size() - 1; ++i)
+ {
+ if(t <= double(i+1))
+ {
+ segment = i;
+ break;
+ }
+ }
+ t -= segment;
+
+ const double reciprocal_alpha = 1.0 / 3.0;
+
+ Vector3 bezierPoints[4];
+ bezierPoints[0] = controlPoints[segment];
+ bezierPoints[1] = (segment > 0)
+ ? controlPoints[segment] + vector3_scaled(controlPoints[segment + 1] - controlPoints[segment - 1], reciprocal_alpha * 0.5)
+ : controlPoints[segment] + vector3_scaled(controlPoints[segment + 1] - controlPoints[segment], reciprocal_alpha);
+ bezierPoints[2] = (segment < controlPoints.size() - 2)
+ ? controlPoints[segment + 1] + vector3_scaled(controlPoints[segment] - controlPoints[segment + 2], reciprocal_alpha * 0.5)
+ : controlPoints[segment + 1] + vector3_scaled(controlPoints[segment] - controlPoints[segment + 1], reciprocal_alpha);
+ bezierPoints[3] = controlPoints[segment + 1];
+ return CubicBezier_evaluate(bezierPoints, t);
+}
+
+typedef Array<float> Knots;
+
+inline double BSpline_basis(const Knots& knots, std::size_t i, std::size_t degree, double t)
+{
+ if(degree == 0)
+ {
+ if(knots[i] <= t
+ && t < knots[i + 1]
+ && knots[i] < knots[i + 1])
+ {
+ return 1;
+ }
+ return 0;
+ }
+ double leftDenom = knots[i + degree] - knots[i];
+ double left = (leftDenom == 0) ? 0 : ((t - knots[i]) / leftDenom) * BSpline_basis(knots, i, degree - 1, t);
+ double rightDenom = knots[i + degree + 1] - knots[i + 1];
+ double right = (rightDenom == 0) ? 0 : ((knots[i + degree + 1] - t) / rightDenom) * BSpline_basis(knots, i + 1, degree - 1, t);
+ return left + right;
+}
+
+inline Vector3 BSpline_evaluate(const ControlPoints& controlPoints, const Knots& knots, std::size_t degree, double t)
+{
+ Vector3 result(0, 0, 0);
+ for(std::size_t i = 0; i < controlPoints.size(); ++i)
+ {
+ result += vector3_scaled(controlPoints[i], BSpline_basis(knots, i, degree, t));
+ }
+ return result;
+}
+
+typedef Array<float> NURBSWeights;
+
+inline Vector3 NURBS_evaluate(const ControlPoints& controlPoints, const NURBSWeights& weights, const Knots& knots, std::size_t degree, double t)
+{
+ Vector3 result(0, 0, 0);
+ double denominator = 0;
+ for(std::size_t i = 0; i < controlPoints.size(); ++i)
+ {
+ double weight = weights[i] * BSpline_basis(knots, i, degree, t);
+ result += vector3_scaled(controlPoints[i], weight);
+ denominator += weight;
+ }
+ return result / denominator;
+}
+
+inline void KnotVector_openUniform(Knots& knots, std::size_t count, std::size_t degree)
+{
+ knots.resize(count + degree + 1);
+
+ std::size_t equalKnots = 1;
+
+ for(std::size_t i = 0; i < equalKnots; ++i)
+ {
+ knots[i] = 0;
+ knots[knots.size() - (i + 1)] = 1;
+ }
+
+ std::size_t difference = knots.size() - 2 * (equalKnots);
+ for(std::size_t i = 0; i < difference; ++i)
+ {
+ knots[i + equalKnots] = Knots::value_type(double(i + 1) * 1.0 / double(difference + 1));
+ }
+}
+
+#endif
projects / voretournament / voretournament.git / blobdiff