mirror of https://github.com/mosra/magnum.git
Ashwin Ravichandran
10 years ago
4 changed files with 199 additions and 0 deletions
@ -0,0 +1,117 @@
|
||||
#ifndef Magnum_Math_Bezier_h |
||||
#define Magnum_Math_Bezier_h |
||||
|
||||
/*
|
||||
This file is part of Magnum. |
||||
|
||||
Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016 |
||||
Vladimír Vondruš <mosra@centrum.cz> |
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a |
||||
copy of this software and associated documentation files (the "Software"), |
||||
to deal in the Software without restriction, including without limitation |
||||
the rights to use, copy, modify, merge, publish, distribute, sublicense, |
||||
and/or sell copies of the Software, and to permit persons to whom the |
||||
Software is furnished to do so, subject to the following conditions: |
||||
|
||||
The above copyright notice and this permission notice shall be included |
||||
in all copies or substantial portions of the Software. |
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
||||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
||||
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING |
||||
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER |
||||
DEALINGS IN THE SOFTWARE. |
||||
*/ |
||||
|
||||
/** @file
|
||||
* @brief Class @ref Magnum::Math::Bezier |
||||
*/ |
||||
|
||||
#include <vector> |
||||
#include "Vector.h" |
||||
|
||||
namespace Magnum { namespace Math { |
||||
/**
|
||||
@brief Bezier |
||||
@tparam order Order of Bezier curve |
||||
@tparam dimensions Dimensions of the control points |
||||
@tparam T Underlying data type |
||||
|
||||
See <a href="https://en.wikipedia.org/wiki/B%C3%A9zier_curve">Bezier Curve</a>. |
||||
*/ |
||||
template<UnsignedInt order, UnsignedInt dimensions, class T> class Bezier { |
||||
|
||||
public: |
||||
|
||||
/** @brief Construct Bezier curve with the given array of control points */ |
||||
explicit Bezier(const std::array<Vector<dimensions, T>, order+1> &points) { |
||||
_points = points; |
||||
} |
||||
|
||||
/**
|
||||
* @brief Divides a Bezier curve into two curves of same order having their own control points. |
||||
* De Casteljau's algorithm is used. |
||||
* @param t The interpolation factor |
||||
* |
||||
* @return Array of two Bezier curves of the same order |
||||
*/ |
||||
std::array<Bezier<order, dimensions, T >, 2> subdivide(Float t) const { |
||||
auto i_points = calculateIntermediatePoints(t); |
||||
std::array<Vector<dimensions, T>, order + 1> left, right; |
||||
for(UnsignedInt i=0; i<=order; ++i){ |
||||
left[i] = i_points[0][i]; |
||||
} |
||||
for(UnsignedInt i = 0, j = order; j>=0; --j, ++i){ |
||||
right[i] = i_points[i][j]; |
||||
} |
||||
return {Bezier<order, dimensions, T>(left), Bezier<order, dimensions, T>(right)}; |
||||
} |
||||
|
||||
/**
|
||||
* @brief Finds the point in the curve for a given interpolation factor |
||||
* De Casteljau's algorithm is used. |
||||
* @param t The interpolation factor |
||||
*/ |
||||
Vector<dimensions, T> lerp (Float t) const { |
||||
auto i_points= calculateIntermediatePoints(t); |
||||
return i_points[0][order]; |
||||
}; |
||||
|
||||
private: |
||||
|
||||
/**
|
||||
* @brief Calculates and returns all intermediate points generated when using De Casteljau's algorithm |
||||
* @param t The interpolation factor |
||||
* |
||||
*/ |
||||
std::vector<std::vector<Vector<dimensions, T>>> calculateIntermediatePoints(Float t) const { |
||||
const auto n = order + 1; |
||||
std::vector<std::vector<Vector<dimensions,T>>> i_points(n,std::vector<Vector<dimensions,T>>(n)); |
||||
for (UnsignedInt i = 0; i < n; ++i) { |
||||
i_points[i][0] = _points[i]; |
||||
} |
||||
for (UnsignedInt r = 1; r < n; ++r) { |
||||
for (UnsignedInt i = 0; i < n - r; ++i) { |
||||
i_points[i][r] = (1 - t) * i_points[i][r - 1] + t * i_points[i + 1][r - 1]; |
||||
} |
||||
} |
||||
return i_points; |
||||
}; |
||||
|
||||
std::array<Vector<dimensions, T >, order + 1> _points; |
||||
}; |
||||
|
||||
template<UnsignedInt dimensions, class T> using QuadraticBezier = Bezier<2, dimensions, T>; |
||||
template<UnsignedInt dimensions, class T> using CubicBezier = Bezier <3, dimensions, T>; |
||||
template<class T> using QuadraticBezier2D = QuadraticBezier<2, T>; |
||||
template<class T> using QuadraticBezier3D = QuadraticBezier<3, T>; |
||||
template<class T> using CubicBezier2D = CubicBezier<2, T>; |
||||
template<class T> using CubicBezier3D = CubicBezier<3, T>; |
||||
|
||||
} |
||||
|
||||
} |
||||
#endif //Magnum_Math_Bezier_h
|
||||
@ -0,0 +1,80 @@
|
||||
/*
|
||||
This file is part of Magnum. |
||||
|
||||
Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016 |
||||
Vladimír Vondruš <mosra@centrum.cz> |
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a |
||||
copy of this software and associated documentation files (the "Software"), |
||||
to deal in the Software without restriction, including without limitation |
||||
the rights to use, copy, modify, merge, publish, distribute, sublicense, |
||||
and/or sell copies of the Software, and to permit persons to whom the |
||||
Software is furnished to do so, subject to the following conditions: |
||||
|
||||
The above copyright notice and this permission notice shall be included |
||||
in all copies or substantial portions of the Software. |
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
||||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
||||
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING |
||||
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER |
||||
DEALINGS IN THE SOFTWARE. |
||||
*/ |
||||
|
||||
#include <Corrade/TestSuite/Tester.h> |
||||
#include "Magnum/Math/Bezier.h" |
||||
|
||||
namespace Magnum { namespace Math { namespace Test { |
||||
|
||||
struct BezierTest: Corrade::TestSuite::Tester { |
||||
explicit BezierTest(); |
||||
|
||||
void testQuadratic(); |
||||
|
||||
void testCubic(); |
||||
|
||||
}; |
||||
|
||||
BezierTest::BezierTest() { |
||||
addTests({&BezierTest::testQuadratic}); |
||||
addTests({&BezierTest::testCubic}); |
||||
} |
||||
|
||||
template <class T> |
||||
inline T sqr(T t){ return t*t; } |
||||
|
||||
template <class T> |
||||
inline T cube(T t){ return t*t*t; } |
||||
|
||||
|
||||
void BezierTest::testQuadratic() { |
||||
typedef Math::Vector<2, Float> Vector2; |
||||
Vector2 p0(0.0f, 0.0f), p1(10.0f, 15.0f), p2(20.0f, 4.0f); |
||||
std::array<Vector2, 3> points = {p0, p1, p2}; |
||||
QuadraticBezier2D<Float> bezier(points); |
||||
for(Float t = 0.0; t <= 1.0f; t += 0.01f) { |
||||
Vector2 expected = sqr(1-t)*p0 + 2*(1-t)*t*p1 + sqr(t) *p2; |
||||
CORRADE_COMPARE(bezier.lerp(t), expected); |
||||
} |
||||
} |
||||
|
||||
void BezierTest::testCubic() { |
||||
typedef Math::Vector<2, Float> Vector2; |
||||
Vector2 p0(0.0f, 0.0f), p1(10.0f, 15.0f), p2(20.0f, 4.0f), p3(5.0f, -20.0f); |
||||
std::array<Vector2, 4> points = {p0, p1, p2, p3}; |
||||
CubicBezier2D<Float> bezier(points); |
||||
for(Float t = 0.0; t <= 1.0f; t += 0.01f) { |
||||
Vector2 expected = cube(1-t)*p0 |
||||
+ 3*sqr(1-t)*t*p1 |
||||
+ 3*(1-t)*sqr(t) *p2 |
||||
+ cube(t)*p3; |
||||
CORRADE_COMPARE(bezier.lerp(t), expected); |
||||
} |
||||
} |
||||
|
||||
|
||||
}}} |
||||
|
||||
CORRADE_TEST_MAIN(Magnum::Math::Test::BezierTest) |
||||
Loading…
Reference in new issue