/*
* Farseer Physics Engine based on Box2D.XNA port:
* Copyright (c) 2010 Ian Qvist
*
* Box2D.XNA port of Box2D:
* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
*
* Original source Box2D:
* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
*
* 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.
*/
using System.Diagnostics;
using FarseerPhysics.Common;
using FarseerPhysics.Common.Decomposition;
using Microsoft.Xna.Framework;
namespace FarseerPhysics.Collision.Shapes
{
/// <summary>
/// Represents a simple non-selfintersecting convex polygon.
/// If you want to have concave polygons, you will have to use the <see cref="BayazitDecomposer"/> or the <see cref="EarclipDecomposer"/>
/// to decompose the concave polygon into 2 or more convex polygons.
/// </summary>
public class PolygonShape : Shape
{
public Vertices Normals;
public Vertices Vertices;
/// <summary>
/// Initializes a new instance of the <see cref="PolygonShape"/> class.
/// </summary>
/// <param name="vertices">The vertices.</param>
/// <param name="density">The density.</param>
public PolygonShape(Vertices vertices, float density)
: base(density)
{
ShapeType = ShapeType.Polygon;
_radius = Settings.PolygonRadius;
Set(vertices);
}
public PolygonShape(float density)
: base(density)
{
ShapeType = ShapeType.Polygon;
_radius = Settings.PolygonRadius;
Normals = new Vertices();
Vertices = new Vertices();
}
internal PolygonShape()
: base(0)
{
ShapeType = ShapeType.Polygon;
_radius = Settings.PolygonRadius;
Normals = new Vertices();
Vertices = new Vertices();
}
public override int ChildCount
{
get { return 1; }
}
public override Shape Clone()
{
PolygonShape clone = new PolygonShape();
clone.ShapeType = ShapeType;
clone._radius = _radius;
clone._density = _density;
if (Settings.ConserveMemory)
{
clone.Vertices = Vertices;
clone.Normals = Normals;
}
else
{
clone.Vertices = new Vertices(Vertices);
clone.Normals = new Vertices(Normals);
}
clone.MassData = MassData;
return clone;
}
/// <summary>
/// Copy vertices. This assumes the vertices define a convex polygon.
/// It is assumed that the exterior is the the right of each edge.
/// </summary>
/// <param name="vertices">The vertices.</param>
public void Set(Vertices vertices)
{
Debug.Assert(vertices.Count >= 3 && vertices.Count <= Settings.MaxPolygonVertices);
if (Settings.ConserveMemory)
Vertices = vertices;
else
// Copy vertices.
Vertices = new Vertices(vertices);
Normals = new Vertices(vertices.Count);
// Compute normals. Ensure the edges have non-zero length.
for (int i = 0; i < vertices.Count; ++i)
{
int i1 = i;
int i2 = i + 1 < vertices.Count ? i + 1 : 0;
Vector2 edge = Vertices[i2] - Vertices[i1];
Debug.Assert(edge.LengthSquared() > Settings.Epsilon * Settings.Epsilon);
Vector2 temp = new Vector2(edge.Y, -edge.X);
temp.Normalize();
Normals.Add(temp);
}
#if DEBUG
// Ensure the polygon is convex and the interior
// is to the left of each edge.
for (int i = 0; i < Vertices.Count; ++i)
{
int i1 = i;
int i2 = i + 1 < Vertices.Count ? i + 1 : 0;
Vector2 edge = Vertices[i2] - Vertices[i1];
for (int j = 0; j < vertices.Count; ++j)
{
// Don't check vertices on the current edge.
if (j == i1 || j == i2)
{
continue;
}
Vector2 r = Vertices[j] - Vertices[i1];
// Your polygon is non-convex (it has an indentation) or
// has colinear edges.
float s = edge.X * r.Y - edge.Y * r.X;
Debug.Assert(s > 0.0f);
}
}
#endif
// Compute the polygon mass data
ComputeProperties();
}
/// <summary>
/// Compute the mass properties of this shape using its dimensions and density.
/// The inertia tensor is computed about the local origin, not the centroid.
/// </summary>
public override void ComputeProperties()
{
// 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.
Debug.Assert(Vertices.Count >= 3);
if (_density <= 0)
return;
Vector2 center = Vector2.Zero;
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).
Vector2 pRef = Vector2.Zero;
#if false
// This code would put the reference point inside the polygon.
for (int i = 0; i < count; ++i)
{
pRef += vs[i];
}
pRef *= 1.0f / count;
#endif
const float inv3 = 1.0f / 3.0f;
for (int i = 0; i < Vertices.Count; ++i)
{
// Triangle vertices.
Vector2 p1 = pRef;
Vector2 p2 = Vertices[i];
Vector2 p3 = i + 1 < Vertices.Count ? Vertices[i + 1] : Vertices[0];
Vector2 e1 = p2 - p1;
Vector2 e2 = p3 - p1;
float d;
MathUtils.Cross(ref e1, ref e2, out d);
float triangleArea = 0.5f * d;
area += triangleArea;
// Area weighted centroid
center += triangleArea * inv3 * (p1 + p2 + p3);
float px = p1.X, py = p1.Y;
float ex1 = e1.X, ey1 = e1.Y;
float ex2 = e2.X, ey2 = e2.Y;
float intx2 = inv3 * (0.25f * (ex1 * ex1 + ex2 * ex1 + ex2 * ex2) + (px * ex1 + px * ex2)) +
0.5f * px * px;
float inty2 = inv3 * (0.25f * (ey1 * ey1 + ey2 * ey1 + ey2 * ey2) + (py * ey1 + py * ey2)) +
0.5f * py * py;
I += d * (intx2 + inty2);
}
//The area is too small for the engine to handle.
Debug.Assert(area > Settings.Epsilon);
// We save the area
MassData.Area = area;
// Total mass
MassData.Mass = _density * area;
// Center of mass
center *= 1.0f / area;
MassData.Centroid = center;
// Inertia tensor relative to the local origin.
MassData.Inertia = _density * I;
}
/// <summary>
/// Build vertices to represent an axis-aligned box.
/// </summary>
/// <param name="halfWidth">The half-width.</param>
/// <param name="halfHeight">The half-height.</param>
public void SetAsBox(float halfWidth, float halfHeight)
{
Set(PolygonTools.CreateRectangle(halfWidth, halfHeight));
}
/// <summary>
/// Build vertices to represent an oriented box.
/// </summary>
/// <param name="halfWidth">The half-width..</param>
/// <param name="halfHeight">The half-height.</param>
/// <param name="center">The center of the box in local coordinates.</param>
/// <param name="angle">The rotation of the box in local coordinates.</param>
public void SetAsBox(float halfWidth, float halfHeight, Vector2 center, float angle)
{
Set(PolygonTools.CreateRectangle(halfWidth, halfHeight, center, angle));
}
/// <summary>
/// Test a point for containment in this shape. This only works for convex shapes.
/// </summary>
/// <param name="transform">The shape world transform.</param>
/// <param name="point">a point in world coordinates.</param>
/// <returns>True if the point is inside the shape</returns>
public override bool TestPoint(ref Transform transform, ref Vector2 point)
{
Vector2 pLocal = MathUtils.MultiplyT(ref transform.R, point - transform.Position);
for (int i = 0; i < Vertices.Count; ++i)
{
float dot = Vector2.Dot(Normals[i], pLocal - Vertices[i]);
if (dot > 0.0f)
{
return false;
}
}
return true;
}
/// <summary>
/// Cast a ray against a child shape.
/// </summary>
/// <param name="output">The ray-cast results.</param>
/// <param name="input">The ray-cast input parameters.</param>
/// <param name="transform">The transform to be applied to the shape.</param>
/// <param name="childIndex">The child shape index.</param>
/// <returns>True if the ray-cast hits the shape</returns>
public override bool RayCast(out RayCastOutput output, ref RayCastInput input, ref Transform transform,
int childIndex)
{
output = new RayCastOutput();
// Put the ray into the polygon's frame of reference.
Vector2 p1 = MathUtils.MultiplyT(ref transform.R, input.Point1 - transform.Position);
Vector2 p2 = MathUtils.MultiplyT(ref transform.R, input.Point2 - transform.Position);
Vector2 d = p2 - p1;
float lower = 0.0f, upper = input.MaxFraction;
int index = -1;
for (int i = 0; i < Vertices.Count; ++i)
{
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
float numerator = Vector2.Dot(Normals[i], Vertices[i] - p1);
float denominator = Vector2.Dot(Normals[i], d);
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;
}
}
// The use of epsilon here causes the assert on lower to trip
// in some cases. Apparently the use of epsilon was to make edge
// shapes work, but now those are handled separately.
//if (upper < lower - b2_epsilon)
if (upper < lower)
{
return false;
}
}
Debug.Assert(0.0f <= lower && lower <= input.MaxFraction);
if (index >= 0)
{
output.Fraction = lower;
output.Normal = MathUtils.Multiply(ref transform.R, Normals[index]);
return true;
}
return false;
}
/// <summary>
/// Given a transform, compute the associated axis aligned bounding box for a child shape.
/// </summary>
/// <param name="aabb">The aabb results.</param>
/// <param name="transform">The world transform of the shape.</param>
/// <param name="childIndex">The child shape index.</param>
public override void ComputeAABB(out AABB aabb, ref Transform transform, int childIndex)
{
Vector2 lower = MathUtils.Multiply(ref transform, Vertices[0]);
Vector2 upper = lower;
for (int i = 1; i < Vertices.Count; ++i)
{
Vector2 v = MathUtils.Multiply(ref transform, Vertices[i]);
lower = Vector2.Min(lower, v);
upper = Vector2.Max(upper, v);
}
Vector2 r = new Vector2(Radius, Radius);
aabb.LowerBound = lower - r;
aabb.UpperBound = upper + r;
}
public bool CompareTo(PolygonShape shape)
{
if (Vertices.Count != shape.Vertices.Count)
return false;
for (int i = 0; i < Vertices.Count; i++)
{
if (Vertices[i] != shape.Vertices[i])
return false;
}
return (Radius == shape.Radius &&
MassData == shape.MassData);
}
public override float ComputeSubmergedArea(Vector2 normal, float offset, Transform xf, out Vector2 sc)
{
sc = Vector2.Zero;
//Transform plane into shape co-ordinates
Vector2 normalL = MathUtils.MultiplyT(ref xf.R, normal);
float offsetL = offset - Vector2.Dot(normal, xf.Position);
float[] depths = new float[Settings.MaxPolygonVertices];
int diveCount = 0;
int intoIndex = -1;
int outoIndex = -1;
bool lastSubmerged = false;
int i;
for (i = 0; i < Vertices.Count; i++)
{
depths[i] = Vector2.Dot(normalL, Vertices[i]) - offsetL;
bool isSubmerged = depths[i] < -Settings.Epsilon;
if (i > 0)
{
if (isSubmerged)
{
if (!lastSubmerged)
{
intoIndex = i - 1;
diveCount++;
}
}
else
{
if (lastSubmerged)
{
outoIndex = i - 1;
diveCount++;
}
}
}
lastSubmerged = isSubmerged;
}
switch (diveCount)
{
case 0:
if (lastSubmerged)
{
//Completely submerged
sc = MathUtils.Multiply(ref xf, MassData.Centroid);
return MassData.Mass / Density;
}
else
{
//Completely dry
return 0;
}
break;
case 1:
if (intoIndex == -1)
{
intoIndex = Vertices.Count - 1;
}
else
{
outoIndex = Vertices.Count - 1;
}
break;
}
int intoIndex2 = (intoIndex + 1) % Vertices.Count;
int outoIndex2 = (outoIndex + 1) % Vertices.Count;
float intoLambda = (0 - depths[intoIndex]) / (depths[intoIndex2] - depths[intoIndex]);
float outoLambda = (0 - depths[outoIndex]) / (depths[outoIndex2] - depths[outoIndex]);
Vector2 intoVec = new Vector2(
Vertices[intoIndex].X * (1 - intoLambda) + Vertices[intoIndex2].X * intoLambda,
Vertices[intoIndex].Y * (1 - intoLambda) + Vertices[intoIndex2].Y * intoLambda);
Vector2 outoVec = new Vector2(
Vertices[outoIndex].X * (1 - outoLambda) + Vertices[outoIndex2].X * outoLambda,
Vertices[outoIndex].Y * (1 - outoLambda) + Vertices[outoIndex2].Y * outoLambda);
//Initialize accumulator
float area = 0;
Vector2 center = new Vector2(0, 0);
Vector2 p2 = Vertices[intoIndex2];
Vector2 p3;
float k_inv3 = 1.0f / 3.0f;
//An awkward loop from intoIndex2+1 to outIndex2
i = intoIndex2;
while (i != outoIndex2)
{
i = (i + 1) % Vertices.Count;
if (i == outoIndex2)
p3 = outoVec;
else
p3 = Vertices[i];
//Add the triangle formed by intoVec,p2,p3
{
Vector2 e1 = p2 - intoVec;
Vector2 e2 = p3 - intoVec;
float D = MathUtils.Cross(e1, e2);
float triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (intoVec + p2 + p3);
}
//
p2 = p3;
}
//Normalize and transform centroid
center *= 1.0f / area;
sc = MathUtils.Multiply(ref xf, center);
return area;
}
}
}
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