/*******************************************************************************
* Copyright (c) 2013, Daniel Murphy
* All rights reserved.
*
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* are permitted provided that the following conditions are met:
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* this list of conditions and the following disclaimer.
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package org.jbox2d.collision.shapes;
import org.jbox2d.collision.AABB;
import org.jbox2d.collision.RayCastInput;
import org.jbox2d.collision.RayCastOutput;
import org.jbox2d.common.MathUtils;
import org.jbox2d.common.Rot;
import org.jbox2d.common.Settings;
import org.jbox2d.common.Transform;
import org.jbox2d.common.Vec2;
import org.jbox2d.pooling.arrays.IntArray;
import org.jbox2d.pooling.arrays.Vec2Array;
/**
* A convex polygon shape. Polygons have a maximum number of vertices equal to _maxPolygonVertices.
* In most cases you should not need many vertices for a convex polygon.
*/
public class PolygonShape extends Shape {
/** Dump lots of debug information. */
private final static boolean m_debug = false;
/**
* Local position of the shape centroid in parent body frame.
*/
public final Vec2 m_centroid = new Vec2();
/**
* The vertices of the shape. Note: use getVertexCount(), not m_vertices.length, to get number of
* active vertices.
*/
public final Vec2 m_vertices[];
/**
* The normals of the shape. Note: use getVertexCount(), not m_normals.length, to get number of
* active normals.
*/
public final Vec2 m_normals[];
/**
* Number of active vertices in the shape.
*/
public int m_count;
// pooling
private final Vec2 pool1 = new Vec2();
private final Vec2 pool2 = new Vec2();
private final Vec2 pool3 = new Vec2();
private final Vec2 pool4 = new Vec2();
private Transform poolt1 = new Transform();
public PolygonShape() {
super(ShapeType.POLYGON);
m_count = 0;
m_vertices = new Vec2[Settings.maxPolygonVertices];
for (int i = 0; i < m_vertices.length; i++) {
m_vertices[i] = new Vec2();
}
m_normals = new Vec2[Settings.maxPolygonVertices];
for (int i = 0; i < m_normals.length; i++) {
m_normals[i] = new Vec2();
}
setRadius(Settings.polygonRadius);
m_centroid.setZero();
}
public final Shape clone() {
PolygonShape shape = new PolygonShape();
shape.m_centroid.set(this.m_centroid);
for (int i = 0; i < shape.m_normals.length; i++) {
shape.m_normals[i].set(m_normals[i]);
shape.m_vertices[i].set(m_vertices[i]);
}
shape.setRadius(this.getRadius());
shape.m_count = this.m_count;
return shape;
}
/**
* Create a convex hull from the given array of points. The count must be in the range [3,
* Settings.maxPolygonVertices].
*
* @warning the points may be re-ordered, even if they form a convex polygon.
* @warning collinear points are removed.
*/
public final void set(final Vec2[] vertices, final int count) {
set(vertices, count, null, null);
}
/**
* Create a convex hull from the given array of points. The count must be in the range [3,
* Settings.maxPolygonVertices]. This method takes an arraypool for pooling.
*
* @warning the points may be re-ordered, even if they form a convex polygon.
* @warning collinear points are removed.
*/
public final void set(final Vec2[] verts, final int num, final Vec2Array vecPool,
final IntArray intPool) {
assert (3 <= num && num <= Settings.maxPolygonVertices);
if (num < 3) {
setAsBox(1.0f, 1.0f);
return;
}
int n = MathUtils.min(num, Settings.maxPolygonVertices);
// Perform welding and copy vertices into local buffer.
Vec2[] ps =
(vecPool != null)
? vecPool.get(Settings.maxPolygonVertices)
: new Vec2[Settings.maxPolygonVertices];
int tempCount = 0;
for (int i = 0; i < n; ++i) {
Vec2 v = verts[i];
boolean unique = true;
for (int j = 0; j < tempCount; ++j) {
if (MathUtils.distanceSquared(v, ps[j]) < 0.5f * Settings.linearSlop) {
unique = false;
break;
}
}
if (unique) {
ps[tempCount++] = v;
}
}
n = tempCount;
if (n < 3) {
// Polygon is degenerate.
assert (false);
setAsBox(1.0f, 1.0f);
return;
}
// Create the convex hull using the Gift wrapping algorithm
// http://en.wikipedia.org/wiki/Gift_wrapping_algorithm
// Find the right most point on the hull
int i0 = 0;
float x0 = ps[0].x;
for (int i = 1; i < n; ++i) {
float x = ps[i].x;
if (x > x0 || (x == x0 && ps[i].y < ps[i0].y)) {
i0 = i;
x0 = x;
}
}
int[] hull =
(intPool != null)
? intPool.get(Settings.maxPolygonVertices)
: new int[Settings.maxPolygonVertices];
int m = 0;
int ih = i0;
while (true) {
hull[m] = ih;
int ie = 0;
for (int j = 1; j < n; ++j) {
if (ie == ih) {
ie = j;
continue;
}
Vec2 r = pool1.set(ps[ie]).subLocal(ps[hull[m]]);
Vec2 v = pool2.set(ps[j]).subLocal(ps[hull[m]]);
float c = Vec2.cross(r, v);
if (c < 0.0f) {
ie = j;
}
// Collinearity check
if (c == 0.0f && v.lengthSquared() > r.lengthSquared()) {
ie = j;
}
}
++m;
ih = ie;
if (ie == i0) {
break;
}
}
this.m_count = m;
// Copy vertices.
for (int i = 0; i < m_count; ++i) {
if (m_vertices[i] == null) {
m_vertices[i] = new Vec2();
}
m_vertices[i].set(ps[hull[i]]);
}
final Vec2 edge = pool1;
// Compute normals. Ensure the edges have non-zero length.
for (int i = 0; i < m_count; ++i) {
final int i1 = i;
final int i2 = i + 1 < m_count ? i + 1 : 0;
edge.set(m_vertices[i2]).subLocal(m_vertices[i1]);
assert (edge.lengthSquared() > Settings.EPSILON * Settings.EPSILON);
Vec2.crossToOutUnsafe(edge, 1f, m_normals[i]);
m_normals[i].normalize();
}
// Compute the polygon centroid.
computeCentroidToOut(m_vertices, m_count, m_centroid);
}
/**
* Build vertices to represent an axis-aligned box.
*
* @param hx the half-width.
* @param hy the half-height.
*/
public final void setAsBox(final float hx, final float hy) {
m_count = 4;
m_vertices[0].set(-hx, -hy);
m_vertices[1].set(hx, -hy);
m_vertices[2].set(hx, hy);
m_vertices[3].set(-hx, hy);
m_normals[0].set(0.0f, -1.0f);
m_normals[1].set(1.0f, 0.0f);
m_normals[2].set(0.0f, 1.0f);
m_normals[3].set(-1.0f, 0.0f);
m_centroid.setZero();
}
/**
* Build vertices to represent an oriented box.
*
* @param hx the half-width.
* @param hy the half-height.
* @param center the center of the box in local coordinates.
* @param angle the rotation of the box in local coordinates.
*/
public final void setAsBox(final float hx, final float hy, final Vec2 center, final float angle) {
m_count = 4;
m_vertices[0].set(-hx, -hy);
m_vertices[1].set(hx, -hy);
m_vertices[2].set(hx, hy);
m_vertices[3].set(-hx, hy);
m_normals[0].set(0.0f, -1.0f);
m_normals[1].set(1.0f, 0.0f);
m_normals[2].set(0.0f, 1.0f);
m_normals[3].set(-1.0f, 0.0f);
m_centroid.set(center);
final Transform xf = poolt1;
xf.p.set(center);
xf.q.set(angle);
// Transform vertices and normals.
for (int i = 0; i < m_count; ++i) {
Transform.mulToOut(xf, m_vertices[i], m_vertices[i]);
Rot.mulToOut(xf.q, m_normals[i], m_normals[i]);
}
}
public int getChildCount() {
return 1;
}
@Override
public final boolean testPoint(final Transform xf, final Vec2 p) {
float tempx, tempy;
final Rot xfq = xf.q;
tempx = p.x - xf.p.x;
tempy = p.y - xf.p.y;
final float pLocalx = xfq.c * tempx + xfq.s * tempy;
final float pLocaly = -xfq.s * tempx + xfq.c * tempy;
if (m_debug) {
System.out.println("--testPoint debug--");
System.out.println("Vertices: ");
for (int i = 0; i < m_count; ++i) {
System.out.println(m_vertices[i]);
}
System.out.println("pLocal: " + pLocalx + ", " + pLocaly);
}
for (int i = 0; i < m_count; ++i) {
Vec2 vertex = m_vertices[i];
Vec2 normal = m_normals[i];
tempx = pLocalx - vertex.x;
tempy = pLocaly - vertex.y;
final float dot = normal.x * tempx + normal.y * tempy;
if (dot > 0.0f) {
return false;
}
}
return true;
}
@Override
public final void computeAABB(final AABB aabb, final Transform xf, int childIndex) {
final Vec2 lower = aabb.lowerBound;
final Vec2 upper = aabb.upperBound;
final Vec2 v1 = m_vertices[0];
final float xfqc = xf.q.c;
final float xfqs = xf.q.s;
final float xfpx = xf.p.x;
final float xfpy = xf.p.y;
lower.x = (xfqc * v1.x - xfqs * v1.y) + xfpx;
lower.y = (xfqs * v1.x + xfqc * v1.y) + xfpy;
upper.x = lower.x;
upper.y = lower.y;
for (int i = 1; i < m_count; ++i) {
Vec2 v2 = m_vertices[i];
// Vec2 v = Mul(xf, m_vertices[i]);
float vx = (xfqc * v2.x - xfqs * v2.y) + xfpx;
float vy = (xfqs * v2.x + xfqc * v2.y) + xfpy;
lower.x = lower.x < vx ? lower.x : vx;
lower.y = lower.y < vy ? lower.y : vy;
upper.x = upper.x > vx ? upper.x : vx;
upper.y = upper.y > vy ? upper.y : vy;
}
lower.x -= m_radius;
lower.y -= m_radius;
upper.x += m_radius;
upper.y += m_radius;
}
/**
* Get the vertex count.
*
* @return
*/
public final int getVertexCount() {
return m_count;
}
/**
* Get a vertex by index.
*
* @param index
* @return
*/
public final Vec2 getVertex(final int index) {
assert (0 <= index && index < m_count);
return m_vertices[index];
}
@Override
public float computeDistanceToOut(Transform xf, Vec2 p, int childIndex, Vec2 normalOut) {
float xfqc = xf.q.c;
float xfqs = xf.q.s;
float tx = p.x - xf.p.x;
float ty = p.y - xf.p.y;
float pLocalx = xfqc * tx + xfqs * ty;
float pLocaly = -xfqs * tx + xfqc * ty;
float maxDistance = -Float.MAX_VALUE;
float normalForMaxDistanceX = pLocalx;
float normalForMaxDistanceY = pLocaly;
for (int i = 0; i < m_count; ++i) {
Vec2 vertex = m_vertices[i];
Vec2 normal = m_normals[i];
tx = pLocalx - vertex.x;
ty = pLocaly - vertex.y;
float dot = normal.x * tx + normal.y * ty;
if (dot > maxDistance) {
maxDistance = dot;
normalForMaxDistanceX = normal.x;
normalForMaxDistanceY = normal.y;
}
}
float distance;
if (maxDistance > 0) {
float minDistanceX = normalForMaxDistanceX;
float minDistanceY = normalForMaxDistanceY;
float minDistance2 = maxDistance * maxDistance;
for (int i = 0; i < m_count; ++i) {
Vec2 vertex = m_vertices[i];
float distanceVecX = pLocalx - vertex.x;
float distanceVecY = pLocaly - vertex.y;
float distance2 = (distanceVecX * distanceVecX + distanceVecY * distanceVecY);
if (minDistance2 > distance2) {
minDistanceX = distanceVecX;
minDistanceY = distanceVecY;
minDistance2 = distance2;
}
}
distance = MathUtils.sqrt(minDistance2);
normalOut.x = xfqc * minDistanceX - xfqs * minDistanceY;
normalOut.y = xfqs * minDistanceX + xfqc * minDistanceY;
normalOut.normalize();
} else {
distance = maxDistance;
normalOut.x = xfqc * normalForMaxDistanceX - xfqs * normalForMaxDistanceY;
normalOut.y = xfqs * normalForMaxDistanceX + xfqc * normalForMaxDistanceY;
}
return distance;
}
@Override
public final boolean raycast(RayCastOutput output, RayCastInput input, Transform xf,
int childIndex) {
final float xfqc = xf.q.c;
final float xfqs = xf.q.s;
final Vec2 xfp = xf.p;
float tempx, tempy;
// b2Vec2 p1 = b2MulT(xf.q, input.p1 - xf.p);
// b2Vec2 p2 = b2MulT(xf.q, input.p2 - xf.p);
tempx = input.p1.x - xfp.x;
tempy = input.p1.y - xfp.y;
final float p1x = xfqc * tempx + xfqs * tempy;
final float p1y = -xfqs * tempx + xfqc * tempy;
tempx = input.p2.x - xfp.x;
tempy = input.p2.y - xfp.y;
final float p2x = xfqc * tempx + xfqs * tempy;
final float p2y = -xfqs * tempx + xfqc * tempy;
final float dx = p2x - p1x;
final float dy = p2y - p1y;
float lower = 0, upper = input.maxFraction;
int index = -1;
for (int i = 0; i < m_count; ++i) {
Vec2 normal = m_normals[i];
Vec2 vertex = m_vertices[i];
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
float tempxn = vertex.x - p1x;
float tempyn = vertex.y - p1y;
final float numerator = normal.x * tempxn + normal.y * tempyn;
final float denominator = normal.x * dx + normal.y * dy;
if (denominator == 0.0f) {
if (numerator < 0.0f) {
return false;
}
} else {
// Note: we want this predicate without division:
// lower < numerator / denominator, where denominator < 0
// Since denominator < 0, we have to flip the inequality:
// lower < numerator / denominator <==> denominator * lower >
// numerator.
if (denominator < 0.0f && numerator < lower * denominator) {
// Increase lower.
// The segment enters this half-space.
lower = numerator / denominator;
index = i;
} else if (denominator > 0.0f && numerator < upper * denominator) {
// Decrease upper.
// The segment exits this half-space.
upper = numerator / denominator;
}
}
if (upper < lower) {
return false;
}
}
assert (0.0f <= lower && lower <= input.maxFraction);
if (index >= 0) {
output.fraction = lower;
// normal = Mul(xf.R, m_normals[index]);
Vec2 normal = m_normals[index];
Vec2 out = output.normal;
out.x = xfqc * normal.x - xfqs * normal.y;
out.y = xfqs * normal.x + xfqc * normal.y;
return true;
}
return false;
}
public final void computeCentroidToOut(final Vec2[] vs, final int count, final Vec2 out) {
assert (count >= 3);
out.set(0.0f, 0.0f);
float area = 0.0f;
// pRef is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
final Vec2 pRef = pool1;
pRef.setZero();
final Vec2 e1 = pool2;
final Vec2 e2 = pool3;
final float inv3 = 1.0f / 3.0f;
for (int i = 0; i < count; ++i) {
// Triangle vertices.
final Vec2 p1 = pRef;
final Vec2 p2 = vs[i];
final Vec2 p3 = i + 1 < count ? vs[i + 1] : vs[0];
e1.set(p2).subLocal(p1);
e2.set(p3).subLocal(p1);
final float D = Vec2.cross(e1, e2);
final float triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
e1.set(p1).addLocal(p2).addLocal(p3).mulLocal(triangleArea * inv3);
out.addLocal(e1);
}
// Centroid
assert (area > Settings.EPSILON);
out.mulLocal(1.0f / area);
}
public void computeMass(final MassData massData, float density) {
// Polygon mass, centroid, and inertia.
// Let rho be the polygon density in mass per unit area.
// Then:
// mass = rho * int(dA)
// centroid.x = (1/mass) * rho * int(x * dA)
// centroid.y = (1/mass) * rho * int(y * dA)
// I = rho * int((x*x + y*y) * dA)
//
// We can compute these integrals by summing all the integrals
// for each triangle of the polygon. To evaluate the integral
// for a single triangle, we make a change of variables to
// the (u,v) coordinates of the triangle:
// x = x0 + e1x * u + e2x * v
// y = y0 + e1y * u + e2y * v
// where 0 <= u && 0 <= v && u + v <= 1.
//
// We integrate u from [0,1-v] and then v from [0,1].
// We also need to use the Jacobian of the transformation:
// D = cross(e1, e2)
//
// Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
//
// The rest of the derivation is handled by computer algebra.
assert (m_count >= 3);
final Vec2 center = pool1;
center.setZero();
float area = 0.0f;
float I = 0.0f;
// pRef is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
final Vec2 s = pool2;
s.setZero();
// This code would put the reference point inside the polygon.
for (int i = 0; i < m_count; ++i) {
s.addLocal(m_vertices[i]);
}
s.mulLocal(1.0f / m_count);
final float k_inv3 = 1.0f / 3.0f;
final Vec2 e1 = pool3;
final Vec2 e2 = pool4;
for (int i = 0; i < m_count; ++i) {
// Triangle vertices.
e1.set(m_vertices[i]).subLocal(s);
e2.set(s).negateLocal().addLocal(i + 1 < m_count ? m_vertices[i + 1] : m_vertices[0]);
final float D = Vec2.cross(e1, e2);
final float triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center.x += triangleArea * k_inv3 * (e1.x + e2.x);
center.y += triangleArea * k_inv3 * (e1.y + e2.y);
final float ex1 = e1.x, ey1 = e1.y;
final float ex2 = e2.x, ey2 = e2.y;
float intx2 = ex1 * ex1 + ex2 * ex1 + ex2 * ex2;
float inty2 = ey1 * ey1 + ey2 * ey1 + ey2 * ey2;
I += (0.25f * k_inv3 * D) * (intx2 + inty2);
}
// Total mass
massData.mass = density * area;
// Center of mass
assert (area > Settings.EPSILON);
center.mulLocal(1.0f / area);
massData.center.set(center).addLocal(s);
// Inertia tensor relative to the local origin (point s)
massData.I = I * density;
// Shift to center of mass then to original body origin.
massData.I += massData.mass * (Vec2.dot(massData.center, massData.center));
}
/**
* Validate convexity. This is a very time consuming operation.
*
* @return
*/
public boolean validate() {
for (int i = 0; i < m_count; ++i) {
int i1 = i;
int i2 = i < m_count - 1 ? i1 + 1 : 0;
Vec2 p = m_vertices[i1];
Vec2 e = pool1.set(m_vertices[i2]).subLocal(p);
for (int j = 0; j < m_count; ++j) {
if (j == i1 || j == i2) {
continue;
}
Vec2 v = pool2.set(m_vertices[j]).subLocal(p);
float c = Vec2.cross(e, v);
if (c < 0.0f) {
return false;
}
}
}
return true;
}
/** Get the vertices in local coordinates. */
public Vec2[] getVertices() {
return m_vertices;
}
/** Get the edge normal vectors. There is one for each vertex. */
public Vec2[] getNormals() {
return m_normals;
}
/** Get the centroid and apply the supplied transform. */
public Vec2 centroid(final Transform xf) {
return Transform.mul(xf, m_centroid);
}
/** Get the centroid and apply the supplied transform. */
public Vec2 centroidToOut(final Transform xf, final Vec2 out) {
Transform.mulToOutUnsafe(xf, m_centroid, out);
return out;
}
}