45 lines
1.4 KiB
C++
45 lines
1.4 KiB
C++
/// @file Bezier.h
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/// @desc Cubic Bezier Curve impl. using De Casteljau's Method
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/// @author Joshua O'Leary
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/// @edited 20 June 2024
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/// @version 2
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/// @copyright (c) Redacted Software 2024
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/// @license Unlicense - Public Domain
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#pragma once
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// Bezier Method:
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// p = (1-t)^3 * P0 + 3*t*(1-t)^2*P1 + 3*t^2*(1-t)*P2 + t^3*P3;
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// For cubics:
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// p = (1-t)^2 * P0 + 2*(1-t)*t*P1 + t*t*P2;
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// Transcribed from here: explicit form and derivative
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// https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B%C3%A9zier_curves
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#include "J3ML/LinearAlgebra/Vector2.h"
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namespace J3ML::Algorithm
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{
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using namespace J3ML::LinearAlgebra;
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template <typename T>
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inline T Square(T f) { return f * f; }
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template <typename T>
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inline T Cube(T f) { return f * f * f; }
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template <typename T>
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inline T Bezier(float t, const T& p0, const T& p1, const T& p2, const T& p3)
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{
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return Cube(1 - t) * p0 + 3 * Square(1 - t) * t * p1 + 3 * (1 - t) * Square(t) * p2 + Cube(t) * p3;
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}
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inline Vector2 Bezier(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
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// Tangent
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Vector2 BezierDerivative(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
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// Normal
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Vector2 BezierNormal(float t, const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3);
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} |