b2Rope.cpp

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/*
* Copyright (c) 2011 Erin Catto http://box2d.org
*
* This software is provided 'as-is', without any express or implied
* warranty.  In no event will the authors be held liable for any damages
* arising from the use of this software.
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/

#include <Box2D/Rope/b2Rope.h>
#include <Box2D/Common/b2Draw.h>

b2Rope::b2Rope()
{
        m_count = 0;
        m_ps = NULL;
        m_p0s = NULL;
        m_vs = NULL;
        m_ims = NULL;
        m_Ls = NULL;
        m_as = NULL;
        m_gravity.SetZero();
        m_k2 = 1.0f;
        m_k3 = 0.1f;
}

b2Rope::~b2Rope()
{
        b2Free(m_ps);
        b2Free(m_p0s);
        b2Free(m_vs);
        b2Free(m_ims);
        b2Free(m_Ls);
        b2Free(m_as);
}

void b2Rope::Initialize(const b2RopeDef* def)
{
        b2Assert(def->count >= 3);
        m_count = def->count;
        m_ps = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
        m_p0s = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
        m_vs = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
        m_ims = (float32*)b2Alloc(m_count * sizeof(float32));

        for (int32 i = 0; i < m_count; ++i)
        {
                m_ps[i] = def->vertices[i];
                m_p0s[i] = def->vertices[i];
                m_vs[i].SetZero();

                float32 m = def->masses[i];
                if (m > 0.0f)
                {
                        m_ims[i] = 1.0f / m;
                }
                else
                {
                        m_ims[i] = 0.0f;
                }
        }

        int32 count2 = m_count - 1;
        int32 count3 = m_count - 2;
        m_Ls = (float32*)b2Alloc(count2 * sizeof(float32));
        m_as = (float32*)b2Alloc(count3 * sizeof(float32));

        for (int32 i = 0; i < count2; ++i)
        {
                b2Vec2 p1 = m_ps[i];
                b2Vec2 p2 = m_ps[i+1];
                m_Ls[i] = b2Distance(p1, p2);
        }

        for (int32 i = 0; i < count3; ++i)
        {
                b2Vec2 p1 = m_ps[i];
                b2Vec2 p2 = m_ps[i + 1];
                b2Vec2 p3 = m_ps[i + 2];

                b2Vec2 d1 = p2 - p1;
                b2Vec2 d2 = p3 - p2;

                float32 a = b2Cross(d1, d2);
                float32 b = b2Dot(d1, d2);

                m_as[i] = b2Atan2(a, b);
        }

        m_gravity = def->gravity;
        m_damping = def->damping;
        m_k2 = def->k2;
        m_k3 = def->k3;
}

void b2Rope::Step(float32 h, int32 iterations)
{
        if (h == 0.0)
        {
                return;
        }

        float32 d = expf(- h * m_damping);

        for (int32 i = 0; i < m_count; ++i)
        {
                m_p0s[i] = m_ps[i];
                if (m_ims[i] > 0.0f)
                {
                        m_vs[i] += h * m_gravity;
                }
                m_vs[i] *= d;
                m_ps[i] += h * m_vs[i];

        }

        for (int32 i = 0; i < iterations; ++i)
        {
                SolveC2();
                SolveC3();
                SolveC2();
        }

        float32 inv_h = 1.0f / h;
        for (int32 i = 0; i < m_count; ++i)
        {
                m_vs[i] = inv_h * (m_ps[i] - m_p0s[i]);
        }
}

void b2Rope::SolveC2()
{
        int32 count2 = m_count - 1;

        for (int32 i = 0; i < count2; ++i)
        {
                b2Vec2 p1 = m_ps[i];
                b2Vec2 p2 = m_ps[i + 1];

                b2Vec2 d = p2 - p1;
                float32 L = d.Normalize();

                float32 im1 = m_ims[i];
                float32 im2 = m_ims[i + 1];

                if (im1 + im2 == 0.0f)
                {
                        continue;
                }

                float32 s1 = im1 / (im1 + im2);
                float32 s2 = im2 / (im1 + im2);

                p1 -= m_k2 * s1 * (m_Ls[i] - L) * d;
                p2 += m_k2 * s2 * (m_Ls[i] - L) * d;

                m_ps[i] = p1;
                m_ps[i + 1] = p2;
        }
}

void b2Rope::SetAngle(float32 angle)
{
        int32 count3 = m_count - 2;
        for (int32 i = 0; i < count3; ++i)
        {
                m_as[i] = angle;
        }
}

void b2Rope::SolveC3()
{
        int32 count3 = m_count - 2;

        for (int32 i = 0; i < count3; ++i)
        {
                b2Vec2 p1 = m_ps[i];
                b2Vec2 p2 = m_ps[i + 1];
                b2Vec2 p3 = m_ps[i + 2];

                float32 m1 = m_ims[i];
                float32 m2 = m_ims[i + 1];
                float32 m3 = m_ims[i + 2];

                b2Vec2 d1 = p2 - p1;
                b2Vec2 d2 = p3 - p2;

                float32 L1sqr = d1.LengthSquared();
                float32 L2sqr = d2.LengthSquared();

                if (L1sqr * L2sqr == 0.0f)
                {
                        continue;
                }

                float32 a = b2Cross(d1, d2);
                float32 b = b2Dot(d1, d2);

                float32 angle = b2Atan2(a, b);

                b2Vec2 Jd1 = (-1.0f / L1sqr) * d1.Skew();
                b2Vec2 Jd2 = (1.0f / L2sqr) * d2.Skew();

                b2Vec2 J1 = -Jd1;
                b2Vec2 J2 = Jd1 - Jd2;
                b2Vec2 J3 = Jd2;

                float32 mass = m1 * b2Dot(J1, J1) + m2 * b2Dot(J2, J2) + m3 * b2Dot(J3, J3);
                if (mass == 0.0f)
                {
                        continue;
                }

                mass = 1.0f / mass;

                float32 C = angle - m_as[i];

                while (C > b2_pi)
                {
                        angle -= 2 * b2_pi;
                        C = angle - m_as[i];
                }

                while (C < -b2_pi)
                {
                        angle += 2.0f * b2_pi;
                        C = angle - m_as[i];
                }

                float32 impulse = - m_k3 * mass * C;

                p1 += (m1 * impulse) * J1;
                p2 += (m2 * impulse) * J2;
                p3 += (m3 * impulse) * J3;

                m_ps[i] = p1;
                m_ps[i + 1] = p2;
                m_ps[i + 2] = p3;
        }
}

void b2Rope::Draw(b2Draw* draw) const
{
        b2Color c(0.4f, 0.5f, 0.7f);

        for (int32 i = 0; i < m_count - 1; ++i)
        {
                draw->DrawSegment(m_ps[i], m_ps[i+1], c);
        }
}