158 lines
3.4 KiB
C++
158 lines
3.4 KiB
C++
/*
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* Copyright (c) 2016-2016 Irlan Robson http://www.irlan.net
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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#ifndef MASS_SPRING_H
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#define MASS_SPRING_H
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class MassSpring : public Test
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{
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public:
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MassSpring()
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{
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m_x.Set(0.0f, 5.0f, 0.0f);
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m_v.SetZero();
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m_k = 100.0f;
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m_iterations = 0;
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}
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void Solve(float32 h)
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{
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// ODE
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// f(Y) = dY / dt = [v]
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// [-k * x]
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// 1. Apply Implicit Euler
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// Y(t + h) = Y(t) + h * f( Y(t + h) )
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// G( Y(t + h) ) = Y(t + h) - Y(t) - h * f( Y(t + h) ) = 0
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// 2. Solve G = 0
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// Newton-Raphson Iteration
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//
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// Y(t + h) =
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// Y(t + h)_0 - G( Y(t + h)_0 ) / G'( Y(t + h)_0 ) =
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// Y(t + h)_0 - G'( Y(t + h)_0 )^-1 * ( Y(t + h)_0 - Y(t) - h * f( Y(t + h)_0 )
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// G'( Y ) = I - h * del_f / del_Y
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// del_f / del_Y = [del_f1 / del_x del_f1 / del_v] = [0 I]
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// [del_f2 / del_x del_f2 / del_v] [-k * I 0]
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// G'( Y ) = [I 0] - [0 h * I] = [I -h * I]
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// [0 I] [-h * k * I 0] [h * k * I I]
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// Compute Jacobian
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b3Mat33 I = b3Mat33_identity;
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b3Mat33 A, B, C, D;
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A = I;
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B = -h * I;
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C = h * m_k * I;
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D = I;
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// Invert
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// Block matrix inversion
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b3Mat33 invD = b3Inverse(D);
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b3Mat33 B_invD = B * invD;
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b3Mat33 invJ_A = b3Inverse(A - B_invD * C);
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b3Mat33 invJ_B = -invJ_A * B_invD;
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b3Mat33 invJ_C = -invD * C * invJ_A;
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b3Mat33 invJ_D = invD + invD * C * invJ_A * B_invD;
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// Initial guess
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b3Vec3 f1 = m_v;
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b3Vec3 f2 = -m_k * m_x;
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b3Vec3 Y1 = m_x + h * f1;
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b3Vec3 Y2 = m_v + h * f2;
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const float32 kTol = 0.05f;
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const u32 kMaxIterations = 20;
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float32 eps0 = 0.0f;
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float32 eps1 = B3_MAX_FLOAT;
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m_iterations = 0;
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while (m_iterations < kMaxIterations && eps1 > kTol * kTol * eps0)
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{
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// Evaluate f(Y_n-1)
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f1 = Y2;
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f2 = -m_k * Y1;
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// Residual vector
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b3Vec3 G1 = Y1 - m_x - h * f1;
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b3Vec3 G2 = Y2 - m_v - h * f2;
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eps1 = b3Dot(G1, G1) + b3Dot(G2, G2);
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// Solve Ax = b
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b3Vec3 x1 = invJ_A * G1 + invJ_B * G2;
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b3Vec3 x2 = invJ_C * G1 + invJ_D * G2;
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Y1 -= x1;
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Y2 -= x2;
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++m_iterations;
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}
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// Update state
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m_x = Y1;
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m_v = Y2;
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}
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void Step()
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{
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float32 h = g_testSettings->inv_hertz;
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Solve(h);
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g_draw->DrawSolidSphere(m_x, 0.25f, b3Color_white);
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g_draw->DrawSegment(b3Vec3_zero, m_x, b3Color_white);
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g_draw->DrawString(b3Color_white, "Iterations = %u", m_iterations);
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float32 E = 0.5f * b3Dot(m_v, m_v);
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g_draw->DrawString(b3Color_white, "E = %f", E);
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}
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static Test* Create()
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{
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return new MassSpring();
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}
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// State
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b3Vec3 m_x, m_v;
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// Stiffness
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float32 m_k;
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//
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u32 m_iterations;
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};
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#endif |