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using System;
using System.Collections.Generic;
using System.Text;
using OpenSim.Region.Physics.Manager;
namespace OpenSim.Region.Physics.OdePlugin.Meshing
{
// A simplex is a section of a straight line.
// It is defined by its endpoints, i.e. by two vertices
// Operation on vertices are
public class Simplex : IComparable<Simplex>
{
public Vertex v1;
public Vertex v2;
public Simplex(Vertex _v1, Vertex _v2)
{
v1 = _v1;
v2 = _v2;
}
public int CompareTo(Simplex other)
{
Vertex lv1, lv2, ov1, ov2, temp;
lv1 = v1;
lv2 = v2;
ov1 = other.v1;
ov2 = other.v2;
if (lv1 > lv2)
{
temp = lv1;
lv1 = lv2;
lv2 = temp;
}
if (ov1 > ov2)
{
temp = ov1;
ov1 = ov2;
ov2 = temp;
}
if (lv1 > ov1)
{
return 1;
}
if (lv1 < ov1)
{
return -1;
}
if (lv2 > ov2)
{
return 1;
}
if (lv2 < ov2)
{
return -1;
}
return 0;
}
private static void intersectParameter(PhysicsVector p1, PhysicsVector r1, PhysicsVector p2, PhysicsVector r2, ref float lambda, ref float mu)
{
// Intersects two straights
// p1, p2, points on the straight
// r1, r2, directional vectors of the straight. Not necessarily of length 1!
// note, that l, m can be scaled such, that the range 0..1 is mapped to the area between two points,
// thus allowing to decide whether an intersection is between two points
float r1x = r1.X;
float r1y = r1.Y;
float r2x = r2.X;
float r2y = r2.Y;
float denom = r1y*r2x - r1x*r2y;
float p1x = p1.X;
float p1y = p1.Y;
float p2x = p2.X;
float p2y = p2.Y;
float z1=-p2x * r2y + p1x * r2y + (p2y - p1y) * r2x;
float z2=-p2x * r1y + p1x * r1y + (p2y - p1y) * r1x;
if (denom == 0.0f) // Means the straights are parallel. Either no intersection or an infinite number of them
{
if (z1==0.0f) {// Means they are identical -> many, many intersections
lambda = Single.NaN;
mu = Single.NaN;
} else {
lambda = Single.PositiveInfinity;
mu = Single.PositiveInfinity;
}
return;
}
lambda = z1 / denom;
mu = z2 / denom;
}
// Intersects the simplex with another one.
// the borders are used to deal with float inaccuracies
// As a rule of thumb, the borders are
// lowerBorder1 : 0.0
// lowerBorder2 : 0.0
// upperBorder1 : 1.0
// upperBorder2 : 1.0
// Set these to values near the given parameters (e.g. 0.001 instead of 1 to exclude simplex starts safely, or to -0.001 to include them safely)
public static PhysicsVector Intersect(
Simplex s1,
Simplex s2,
float lowerBorder1,
float lowerBorder2,
float upperBorder1,
float upperBorder2)
{
PhysicsVector firstSimplexDirection = s1.v2 - s1.v1;
PhysicsVector secondSimplexDirection = s2.v2 - s2.v1;
float lambda = 0.0f;
float mu = 0.0f;
// Give us the parameters of an intersection. This subroutine does *not* take the constraints
// (intersection must be between v1 and v2 and it must be in the positive direction of the ray)
// into account. We do that afterwards.
intersectParameter(s1.v1, firstSimplexDirection, s2.v1, secondSimplexDirection, ref lambda, ref mu);
if (Single.IsInfinity(lambda)) // Special case. No intersection at all. directions parallel.
return null;
if (Single.IsNaN(lambda)) // Special case. many, many intersections.
return null;
if (lambda > upperBorder1) // We're behind v2
return null;
if (lambda < lowerBorder1)
return null;
if (mu < lowerBorder2) // outside simplex 2
return null;
if (mu > upperBorder2) // outside simplex 2
return null;
return s1.v1 + lambda * firstSimplexDirection;
}
// Intersects the simplex with a ray. The ray is defined as all p=origin + lambda*direction
// where lambda >= 0
public PhysicsVector RayIntersect(Vertex origin, PhysicsVector direction, bool bEndsIncluded)
{
PhysicsVector simplexDirection = v2 - v1;
float lambda = 0.0f;
float mu = 0.0f;
// Give us the parameters of an intersection. This subroutine does *not* take the constraints
// (intersection must be between v1 and v2 and it must be in the positive direction of the ray)
// into account. We do that afterwards.
intersectParameter(v1, simplexDirection, origin, direction, ref lambda, ref mu);
if (Single.IsInfinity(lambda)) // Special case. No intersection at all. directions parallel.
return null;
if (Single.IsNaN(lambda)) // Special case. many, many intersections.
return null;
if (mu < 0.0) // We're on the wrong side of the ray
return null;
if (lambda > 1.0) // We're behind v2
return null;
if (lambda == 1.0 && !bEndsIncluded)
return null; // The end of the simplices are not included
if (lambda < 0.0f) // we're before v1;
return null;
return this.v1 + lambda * simplexDirection;
}
}
}
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