149 lines
4.2 KiB
C
149 lines
4.2 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 B3_TIME_STEP_H
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#define B3_TIME_STEP_H
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#include <bounce/common/math/vec3.h>
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#include <bounce/common/math/mat33.h>
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#include <bounce/common/math/quat.h>
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struct b3Position
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{
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b3Vec3 x;
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b3Quat q;
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};
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struct b3Velocity
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{
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b3Vec3 v;
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b3Vec3 w;
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};
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struct b3SolverData
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{
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b3Position* positions;
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b3Velocity* velocities;
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float32 dt;
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float32 invdt;
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};
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enum b3LimitState
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{
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e_inactiveLimit,
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e_atLowerLimit,
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e_atUpperLimit,
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e_equalLimits
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};
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// Move an inertia tensor from the its current center
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// to another.
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inline b3Mat33 b3MoveToCOM(const b3Mat33& inertia, float32 mass, const b3Vec3& center)
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{
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// Paralell Axis Theorem
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// J = I + m * dot(r, r) * E - outer(r, r)
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// where
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// I - inertia about the center of mass
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// m - mass
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// E - identity 3x3
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// r - displacement vector from the current com to the new com
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// J - inertia tensor at the new center of rotation
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float32 dd = b3Dot(center, center);
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b3Mat33 A = b3Diagonal(mass * dd);
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b3Mat33 B = b3Outer(center, center);
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return inertia + A - B;
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}
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// Compute the inertia matrix of a body measured in
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// inertial frame (variable over time) given the
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// inertia matrix in body-fixed frame (constant)
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// and a rotation matrix representing the orientation
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// of the body frame relative to the inertial frame.
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inline b3Mat33 b3RotateToFrame(const b3Mat33& inertia, const b3Mat33& rotation)
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{
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return rotation * inertia * b3Transpose(rotation);
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}
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// Compute the time derivative of an orientation given
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// the angular velocity of the rotating frame represented by the orientation.
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inline b3Quat b3Derivative(const b3Quat& orientation, const b3Vec3& velocity)
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{
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b3Quat xf(0.5f * velocity.x, 0.5f * velocity.y, 0.5f * velocity.z, 0.0f);
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return xf * orientation;
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}
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// Integrate an orientation over a time step given
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// the current orientation, angular velocity of the rotating frame
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// represented by the orientation, and the time step dt.
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inline b3Quat b3Integrate(const b3Quat& orientation, const b3Vec3& velocity, float32 dt)
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{
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// Integrate from [t0, t0 + h] using the explicit Euler method
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b3Quat qdot = b3Derivative(orientation, velocity);
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b3Quat integral = dt * qdot;
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return orientation + integral;
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}
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// Compute the time derivative of an orientation given
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// the angular velocity of the rotating frame represented by the orientation.
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inline b3Mat33 b3Derivative(const b3Mat33& orientation, const b3Vec3& velocity)
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{
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// Rate of change of a basis in a rotating frame:
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// xdot = cross(w, ex)
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// ydot = cross(w, ey)
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// zdot = cross(w, ez)
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// This should yield in:
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// qdot = skew(velocity) * q
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b3Mat33 xf = b3Skew(velocity);
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return xf * orientation;
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}
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// Integrate an orientation over a time step given
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// the current orientation, angular velocity of the rotating frame
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// represented by the orientation, and the time step dt.
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inline b3Mat33 b3Integrate(const b3Mat33& orientation, const b3Vec3& velocity, float32 dt)
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{
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b3Mat33 qdot = b3Derivative(orientation, velocity);
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b3Mat33 integral = dt * qdot;
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return orientation + integral;
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}
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// These structures contain the elapsed time it took
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// to run particular method.
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struct b3CollideProfile
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{
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float64 broadphase;
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float64 narrowphase;
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};
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struct b3SolverProfile
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{
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float64 initializeContacts;
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float64 initializeJoints;
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float64 solveVelocity;
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float64 solvePosition;
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};
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struct b3Profile
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{
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float64 total;
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b3CollideProfile collide;
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b3SolverProfile solver;
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};
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#endif
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