b2_distance.cpp

Go to the documentation of this file.

// MIT License

// Copyright (c) 2019 Erin Catto

// 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 "box2d/b2_circle_shape.h"
#include "box2d/b2_distance.h"
#include "box2d/b2_edge_shape.h"
#include "box2d/b2_chain_shape.h"
#include "box2d/b2_polygon_shape.h"

// GJK using Voronoi regions (Christer Ericson) and Barycentric coordinates.
B2_API int32 b2_gjkCalls, b2_gjkIters, b2_gjkMaxIters;

void b2DistanceProxy::Set(const b2Shape* shape, int32 index)
{
        switch (shape->GetType())
        {
        case b2Shape::e_circle:
                {
                        const b2CircleShape* circle = static_cast<const b2CircleShape*>(shape);
                        m_vertices = &circle->m_p;
                        m_count = 1;
                        m_radius = circle->m_radius;
                }
                break;

        case b2Shape::e_polygon:
                {
                        const b2PolygonShape* polygon = static_cast<const b2PolygonShape*>(shape);
                        m_vertices = polygon->m_vertices;
                        m_count = polygon->m_count;
                        m_radius = polygon->m_radius;
                }
                break;

        case b2Shape::e_chain:
                {
                        const b2ChainShape* chain = static_cast<const b2ChainShape*>(shape);
                        b2Assert(0 <= index && index < chain->m_count);

                        m_buffer[0] = chain->m_vertices[index];
                        if (index + 1 < chain->m_count)
                        {
                                m_buffer[1] = chain->m_vertices[index + 1];
                        }
                        else
                        {
                                m_buffer[1] = chain->m_vertices[0];
                        }

                        m_vertices = m_buffer;
                        m_count = 2;
                        m_radius = chain->m_radius;
                }
                break;

        case b2Shape::e_edge:
                {
                        const b2EdgeShape* edge = static_cast<const b2EdgeShape*>(shape);
                        m_vertices = &edge->m_vertex1;
                        m_count = 2;
                        m_radius = edge->m_radius;
                }
                break;

        default:
                b2Assert(false);
        }
}

void b2DistanceProxy::Set(const b2Vec2* vertices, int32 count, float radius)
{
    m_vertices = vertices;
    m_count = count;
    m_radius = radius;
}

struct b2SimplexVertex
{
        b2Vec2 wA;              // support point in proxyA
        b2Vec2 wB;              // support point in proxyB
        b2Vec2 w;               // wB - wA
        float a;                // barycentric coordinate for closest point
        int32 indexA;   // wA index
        int32 indexB;   // wB index
};

struct b2Simplex
{
        void ReadCache( const b2SimplexCache* cache,
                                        const b2DistanceProxy* proxyA, const b2Transform& transformA,
                                        const b2DistanceProxy* proxyB, const b2Transform& transformB)
        {
                b2Assert(cache->count <= 3);
                
                // Copy data from cache.
                m_count = cache->count;
                b2SimplexVertex* vertices = &m_v1;
                for (int32 i = 0; i < m_count; ++i)
                {
                        b2SimplexVertex* v = vertices + i;
                        v->indexA = cache->indexA[i];
                        v->indexB = cache->indexB[i];
                        b2Vec2 wALocal = proxyA->GetVertex(v->indexA);
                        b2Vec2 wBLocal = proxyB->GetVertex(v->indexB);
                        v->wA = b2Mul(transformA, wALocal);
                        v->wB = b2Mul(transformB, wBLocal);
                        v->w = v->wB - v->wA;
                        v->a = 0.0f;
                }

                // Compute the new simplex metric, if it is substantially different than
                // old metric then flush the simplex.
                if (m_count > 1)
                {
                        float metric1 = cache->metric;
                        float metric2 = GetMetric();
                        if (metric2 < 0.5f * metric1 || 2.0f * metric1 < metric2 || metric2 < b2_epsilon)
                        {
                                // Reset the simplex.
                                m_count = 0;
                        }
                }

                // If the cache is empty or invalid ...
                if (m_count == 0)
                {
                        b2SimplexVertex* v = vertices + 0;
                        v->indexA = 0;
                        v->indexB = 0;
                        b2Vec2 wALocal = proxyA->GetVertex(0);
                        b2Vec2 wBLocal = proxyB->GetVertex(0);
                        v->wA = b2Mul(transformA, wALocal);
                        v->wB = b2Mul(transformB, wBLocal);
                        v->w = v->wB - v->wA;
                        v->a = 1.0f;
                        m_count = 1;
                }
        }

        void WriteCache(b2SimplexCache* cache) const
        {
                cache->metric = GetMetric();
                cache->count = uint16(m_count);
                const b2SimplexVertex* vertices = &m_v1;
                for (int32 i = 0; i < m_count; ++i)
                {
                        cache->indexA[i] = uint8(vertices[i].indexA);
                        cache->indexB[i] = uint8(vertices[i].indexB);
                }
        }

        b2Vec2 GetSearchDirection() const
        {
                switch (m_count)
                {
                case 1:
                        return -m_v1.w;

                case 2:
                        {
                                b2Vec2 e12 = m_v2.w - m_v1.w;
                                float sgn = b2Cross(e12, -m_v1.w);
                                if (sgn > 0.0f)
                                {
                                        // Origin is left of e12.
                                        return b2Cross(1.0f, e12);
                                }
                                else
                                {
                                        // Origin is right of e12.
                                        return b2Cross(e12, 1.0f);
                                }
                        }

                default:
                        b2Assert(false);
                        return b2Vec2_zero;
                }
        }

        b2Vec2 GetClosestPoint() const
        {
                switch (m_count)
                {
                case 0:
                        b2Assert(false);
                        return b2Vec2_zero;

                case 1:
                        return m_v1.w;

                case 2:
                        return m_v1.a * m_v1.w + m_v2.a * m_v2.w;

                case 3:
                        return b2Vec2_zero;

                default:
                        b2Assert(false);
                        return b2Vec2_zero;
                }
        }

        void GetWitnessPoints(b2Vec2* pA, b2Vec2* pB) const
        {
                switch (m_count)
                {
                case 0:
                        b2Assert(false);
                        break;

                case 1:
                        *pA = m_v1.wA;
                        *pB = m_v1.wB;
                        break;

                case 2:
                        *pA = m_v1.a * m_v1.wA + m_v2.a * m_v2.wA;
                        *pB = m_v1.a * m_v1.wB + m_v2.a * m_v2.wB;
                        break;

                case 3:
                        *pA = m_v1.a * m_v1.wA + m_v2.a * m_v2.wA + m_v3.a * m_v3.wA;
                        *pB = *pA;
                        break;

                default:
                        b2Assert(false);
                        break;
                }
        }

        float GetMetric() const
        {
                switch (m_count)
                {
                case 0:
                        b2Assert(false);
                        return 0.0f;

                case 1:
                        return 0.0f;

                case 2:
                        return b2Distance(m_v1.w, m_v2.w);

                case 3:
                        return b2Cross(m_v2.w - m_v1.w, m_v3.w - m_v1.w);

                default:
                        b2Assert(false);
                        return 0.0f;
                }
        }

        void Solve2();
        void Solve3();

        b2SimplexVertex m_v1, m_v2, m_v3;
        int32 m_count;
};


// Solve a line segment using barycentric coordinates.
//
// p = a1 * w1 + a2 * w2
// a1 + a2 = 1
//
// The vector from the origin to the closest point on the line is
// perpendicular to the line.
// e12 = w2 - w1
// dot(p, e) = 0
// a1 * dot(w1, e) + a2 * dot(w2, e) = 0
//
// 2-by-2 linear system
// [1      1     ][a1] = [1]
// [w1.e12 w2.e12][a2] = [0]
//
// Define
// d12_1 =  dot(w2, e12)
// d12_2 = -dot(w1, e12)
// d12 = d12_1 + d12_2
//
// Solution
// a1 = d12_1 / d12
// a2 = d12_2 / d12
void b2Simplex::Solve2()
{
        b2Vec2 w1 = m_v1.w;
        b2Vec2 w2 = m_v2.w;
        b2Vec2 e12 = w2 - w1;

        // w1 region
        float d12_2 = -b2Dot(w1, e12);
        if (d12_2 <= 0.0f)
        {
                // a2 <= 0, so we clamp it to 0
                m_v1.a = 1.0f;
                m_count = 1;
                return;
        }

        // w2 region
        float d12_1 = b2Dot(w2, e12);
        if (d12_1 <= 0.0f)
        {
                // a1 <= 0, so we clamp it to 0
                m_v2.a = 1.0f;
                m_count = 1;
                m_v1 = m_v2;
                return;
        }

        // Must be in e12 region.
        float inv_d12 = 1.0f / (d12_1 + d12_2);
        m_v1.a = d12_1 * inv_d12;
        m_v2.a = d12_2 * inv_d12;
        m_count = 2;
}

// Possible regions:
// - points[2]
// - edge points[0]-points[2]
// - edge points[1]-points[2]
// - inside the triangle
void b2Simplex::Solve3()
{
        b2Vec2 w1 = m_v1.w;
        b2Vec2 w2 = m_v2.w;
        b2Vec2 w3 = m_v3.w;

        // Edge12
        // [1      1     ][a1] = [1]
        // [w1.e12 w2.e12][a2] = [0]
        // a3 = 0
        b2Vec2 e12 = w2 - w1;
        float w1e12 = b2Dot(w1, e12);
        float w2e12 = b2Dot(w2, e12);
        float d12_1 = w2e12;
        float d12_2 = -w1e12;

        // Edge13
        // [1      1     ][a1] = [1]
        // [w1.e13 w3.e13][a3] = [0]
        // a2 = 0
        b2Vec2 e13 = w3 - w1;
        float w1e13 = b2Dot(w1, e13);
        float w3e13 = b2Dot(w3, e13);
        float d13_1 = w3e13;
        float d13_2 = -w1e13;

        // Edge23
        // [1      1     ][a2] = [1]
        // [w2.e23 w3.e23][a3] = [0]
        // a1 = 0
        b2Vec2 e23 = w3 - w2;
        float w2e23 = b2Dot(w2, e23);
        float w3e23 = b2Dot(w3, e23);
        float d23_1 = w3e23;
        float d23_2 = -w2e23;
        
        // Triangle123
        float n123 = b2Cross(e12, e13);

        float d123_1 = n123 * b2Cross(w2, w3);
        float d123_2 = n123 * b2Cross(w3, w1);
        float d123_3 = n123 * b2Cross(w1, w2);

        // w1 region
        if (d12_2 <= 0.0f && d13_2 <= 0.0f)
        {
                m_v1.a = 1.0f;
                m_count = 1;
                return;
        }

        // e12
        if (d12_1 > 0.0f && d12_2 > 0.0f && d123_3 <= 0.0f)
        {
                float inv_d12 = 1.0f / (d12_1 + d12_2);
                m_v1.a = d12_1 * inv_d12;
                m_v2.a = d12_2 * inv_d12;
                m_count = 2;
                return;
        }

        // e13
        if (d13_1 > 0.0f && d13_2 > 0.0f && d123_2 <= 0.0f)
        {
                float inv_d13 = 1.0f / (d13_1 + d13_2);
                m_v1.a = d13_1 * inv_d13;
                m_v3.a = d13_2 * inv_d13;
                m_count = 2;
                m_v2 = m_v3;
                return;
        }

        // w2 region
        if (d12_1 <= 0.0f && d23_2 <= 0.0f)
        {
                m_v2.a = 1.0f;
                m_count = 1;
                m_v1 = m_v2;
                return;
        }

        // w3 region
        if (d13_1 <= 0.0f && d23_1 <= 0.0f)
        {
                m_v3.a = 1.0f;
                m_count = 1;
                m_v1 = m_v3;
                return;
        }

        // e23
        if (d23_1 > 0.0f && d23_2 > 0.0f && d123_1 <= 0.0f)
        {
                float inv_d23 = 1.0f / (d23_1 + d23_2);
                m_v2.a = d23_1 * inv_d23;
                m_v3.a = d23_2 * inv_d23;
                m_count = 2;
                m_v1 = m_v3;
                return;
        }

        // Must be in triangle123
        float inv_d123 = 1.0f / (d123_1 + d123_2 + d123_3);
        m_v1.a = d123_1 * inv_d123;
        m_v2.a = d123_2 * inv_d123;
        m_v3.a = d123_3 * inv_d123;
        m_count = 3;
}

void b2Distance(b2DistanceOutput* output,
                                b2SimplexCache* cache,
                                const b2DistanceInput* input)
{
        ++b2_gjkCalls;

        const b2DistanceProxy* proxyA = &input->proxyA;
        const b2DistanceProxy* proxyB = &input->proxyB;

        b2Transform transformA = input->transformA;
        b2Transform transformB = input->transformB;

        // Initialize the simplex.
        b2Simplex simplex;
        simplex.ReadCache(cache, proxyA, transformA, proxyB, transformB);

        // Get simplex vertices as an array.
        b2SimplexVertex* vertices = &simplex.m_v1;
        const int32 k_maxIters = 20;

        // These store the vertices of the last simplex so that we
        // can check for duplicates and prevent cycling.
        int32 saveA[3], saveB[3];
        int32 saveCount = 0;

        // Main iteration loop.
        int32 iter = 0;
        while (iter < k_maxIters)
        {
                // Copy simplex so we can identify duplicates.
                saveCount = simplex.m_count;
                for (int32 i = 0; i < saveCount; ++i)
                {
                        saveA[i] = vertices[i].indexA;
                        saveB[i] = vertices[i].indexB;
                }

                switch (simplex.m_count)
                {
                case 1:
                        break;

                case 2:
                        simplex.Solve2();
                        break;

                case 3:
                        simplex.Solve3();
                        break;

                default:
                        b2Assert(false);
                }

                // If we have 3 points, then the origin is in the corresponding triangle.
                if (simplex.m_count == 3)
                {
                        break;
                }

                // Get search direction.
                b2Vec2 d = simplex.GetSearchDirection();

                // Ensure the search direction is numerically fit.
                if (d.LengthSquared() < b2_epsilon * b2_epsilon)
                {
                        // The origin is probably contained by a line segment
                        // or triangle. Thus the shapes are overlapped.

                        // We can't return zero here even though there may be overlap.
                        // In case the simplex is a point, segment, or triangle it is difficult
                        // to determine if the origin is contained in the CSO or very close to it.
                        break;
                }

                // Compute a tentative new simplex vertex using support points.
                b2SimplexVertex* vertex = vertices + simplex.m_count;
                vertex->indexA = proxyA->GetSupport(b2MulT(transformA.q, -d));
                vertex->wA = b2Mul(transformA, proxyA->GetVertex(vertex->indexA));
                vertex->indexB = proxyB->GetSupport(b2MulT(transformB.q, d));
                vertex->wB = b2Mul(transformB, proxyB->GetVertex(vertex->indexB));
                vertex->w = vertex->wB - vertex->wA;

                // Iteration count is equated to the number of support point calls.
                ++iter;
                ++b2_gjkIters;

                // Check for duplicate support points. This is the main termination criteria.
                bool duplicate = false;
                for (int32 i = 0; i < saveCount; ++i)
                {
                        if (vertex->indexA == saveA[i] && vertex->indexB == saveB[i])
                        {
                                duplicate = true;
                                break;
                        }
                }

                // If we found a duplicate support point we must exit to avoid cycling.
                if (duplicate)
                {
                        break;
                }

                // New vertex is ok and needed.
                ++simplex.m_count;
        }

        b2_gjkMaxIters = b2Max(b2_gjkMaxIters, iter);

        // Prepare output.
        simplex.GetWitnessPoints(&output->pointA, &output->pointB);
        output->distance = b2Distance(output->pointA, output->pointB);
        output->iterations = iter;

        // Cache the simplex.
        simplex.WriteCache(cache);

        // Apply radii if requested.
        if (input->useRadii)
        {
                float rA = proxyA->m_radius;
                float rB = proxyB->m_radius;

                if (output->distance > rA + rB && output->distance > b2_epsilon)
                {
                        // Shapes are still no overlapped.
                        // Move the witness points to the outer surface.
                        output->distance -= rA + rB;
                        b2Vec2 normal = output->pointB - output->pointA;
                        normal.Normalize();
                        output->pointA += rA * normal;
                        output->pointB -= rB * normal;
                }
                else
                {
                        // Shapes are overlapped when radii are considered.
                        // Move the witness points to the middle.
                        b2Vec2 p = 0.5f * (output->pointA + output->pointB);
                        output->pointA = p;
                        output->pointB = p;
                        output->distance = 0.0f;
                }
        }
}

// GJK-raycast
// Algorithm by Gino van den Bergen.
// "Smooth Mesh Contacts with GJK" in Game Physics Pearls. 2010
bool b2ShapeCast(b2ShapeCastOutput * output, const b2ShapeCastInput * input)
{
    output->iterations = 0;
    output->lambda = 1.0f;
    output->normal.SetZero();
    output->point.SetZero();

        const b2DistanceProxy* proxyA = &input->proxyA;
        const b2DistanceProxy* proxyB = &input->proxyB;

    float radiusA = b2Max(proxyA->m_radius, b2_polygonRadius);
    float radiusB = b2Max(proxyB->m_radius, b2_polygonRadius);
    float radius = radiusA + radiusB;

        b2Transform xfA = input->transformA;
        b2Transform xfB = input->transformB;

        b2Vec2 r = input->translationB;
        b2Vec2 n(0.0f, 0.0f);
        float lambda = 0.0f;

        // Initial simplex
        b2Simplex simplex;
        simplex.m_count = 0;

        // Get simplex vertices as an array.
        b2SimplexVertex* vertices = &simplex.m_v1;

        // Get support point in -r direction
        int32 indexA = proxyA->GetSupport(b2MulT(xfA.q, -r));
        b2Vec2 wA = b2Mul(xfA, proxyA->GetVertex(indexA));
        int32 indexB = proxyB->GetSupport(b2MulT(xfB.q, r));
        b2Vec2 wB = b2Mul(xfB, proxyB->GetVertex(indexB));
    b2Vec2 v = wA - wB;

    // Sigma is the target distance between polygons
    float sigma = b2Max(b2_polygonRadius, radius - b2_polygonRadius);
        const float tolerance = 0.5f * b2_linearSlop;

        // Main iteration loop.
        const int32 k_maxIters = 20;
        int32 iter = 0;
        while (iter < k_maxIters && v.Length() - sigma > tolerance)
        {
                b2Assert(simplex.m_count < 3);

        output->iterations += 1;

                // Support in direction -v (A - B)
                indexA = proxyA->GetSupport(b2MulT(xfA.q, -v));
                wA = b2Mul(xfA, proxyA->GetVertex(indexA));
                indexB = proxyB->GetSupport(b2MulT(xfB.q, v));
                wB = b2Mul(xfB, proxyB->GetVertex(indexB));
        b2Vec2 p = wA - wB;

        // -v is a normal at p
        v.Normalize();

        // Intersect ray with plane
                float vp = b2Dot(v, p);
        float vr = b2Dot(v, r);
                if (vp - sigma > lambda * vr)
                {
                        if (vr <= 0.0f)
                        {
                                return false;
                        }

                        lambda = (vp - sigma) / vr;
                        if (lambda > 1.0f)
                        {
                                return false;
                        }

            n = -v;
            simplex.m_count = 0;
                }

        // Reverse simplex since it works with B - A.
        // Shift by lambda * r because we want the closest point to the current clip point.
        // Note that the support point p is not shifted because we want the plane equation
        // to be formed in unshifted space.
                b2SimplexVertex* vertex = vertices + simplex.m_count;
                vertex->indexA = indexB;
                vertex->wA = wB + lambda * r;
                vertex->indexB = indexA;
                vertex->wB = wA;
                vertex->w = vertex->wB - vertex->wA;
                vertex->a = 1.0f;
                simplex.m_count += 1;

                switch (simplex.m_count)
                {
                case 1:
                        break;

                case 2:
                        simplex.Solve2();
                        break;

                case 3:
                        simplex.Solve3();
                        break;

                default:
                        b2Assert(false);
                }
                
                // If we have 3 points, then the origin is in the corresponding triangle.
                if (simplex.m_count == 3)
                {
                        // Overlap
                        return false;
                }

                // Get search direction.
                v = simplex.GetClosestPoint();

                // Iteration count is equated to the number of support point calls.
                ++iter;
        }

        if (iter == 0)
        {
                // Initial overlap
                return false;
        }

        // Prepare output.
        b2Vec2 pointA, pointB;
        simplex.GetWitnessPoints(&pointB, &pointA);

        if (v.LengthSquared() > 0.0f)
        {
        n = -v;
                n.Normalize();
        }

    output->point = pointA + radiusA * n;
        output->normal = n;
        output->lambda = lambda;
        output->iterations = iter;
        return true;
}