opensim-development – Rev 1
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/*
* Copyright (c) Contributors, http://opensimulator.org/
* See CONTRIBUTORS.TXT for a full list of copyright holders.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the OpenSimulator Project nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE DEVELOPERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE CONTRIBUTORS BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using OpenMetaverse;
using OpenSim.Region.Physics.Manager;
using OpenSim.Region.Physics.Meshing;
public class Vertex : IComparable<Vertex>
{
Vector3 vector;
public float X
{
get { return vector.X; }
set { vector.X = value; }
}
public float Y
{
get { return vector.Y; }
set { vector.Y = value; }
}
public float Z
{
get { return vector.Z; }
set { vector.Z = value; }
}
public Vertex(float x, float y, float z)
{
vector.X = x;
vector.Y = y;
vector.Z = z;
}
public Vertex normalize()
{
float tlength = vector.Length();
if (tlength != 0f)
{
float mul = 1.0f / tlength;
return new Vertex(vector.X * mul, vector.Y * mul, vector.Z * mul);
}
else
{
return new Vertex(0f, 0f, 0f);
}
}
public Vertex cross(Vertex v)
{
return new Vertex(vector.Y * v.Z - vector.Z * v.Y, vector.Z * v.X - vector.X * v.Z, vector.X * v.Y - vector.Y * v.X);
}
// disable warning: mono compiler moans about overloading
// operators hiding base operator but should not according to C#
// language spec
#pragma warning disable 0108
public static Vertex operator *(Vertex v, Quaternion q)
{
// From http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/
Vertex v2 = new Vertex(0f, 0f, 0f);
v2.X = q.W * q.W * v.X +
2f * q.Y * q.W * v.Z -
2f * q.Z * q.W * v.Y +
q.X * q.X * v.X +
2f * q.Y * q.X * v.Y +
2f * q.Z * q.X * v.Z -
q.Z * q.Z * v.X -
q.Y * q.Y * v.X;
v2.Y =
2f * q.X * q.Y * v.X +
q.Y * q.Y * v.Y +
2f * q.Z * q.Y * v.Z +
2f * q.W * q.Z * v.X -
q.Z * q.Z * v.Y +
q.W * q.W * v.Y -
2f * q.X * q.W * v.Z -
q.X * q.X * v.Y;
v2.Z =
2f * q.X * q.Z * v.X +
2f * q.Y * q.Z * v.Y +
q.Z * q.Z * v.Z -
2f * q.W * q.Y * v.X -
q.Y * q.Y * v.Z +
2f * q.W * q.X * v.Y -
q.X * q.X * v.Z +
q.W * q.W * v.Z;
return v2;
}
public static Vertex operator +(Vertex v1, Vertex v2)
{
return new Vertex(v1.X + v2.X, v1.Y + v2.Y, v1.Z + v2.Z);
}
public static Vertex operator -(Vertex v1, Vertex v2)
{
return new Vertex(v1.X - v2.X, v1.Y - v2.Y, v1.Z - v2.Z);
}
public static Vertex operator *(Vertex v1, Vertex v2)
{
return new Vertex(v1.X * v2.X, v1.Y * v2.Y, v1.Z * v2.Z);
}
public static Vertex operator +(Vertex v1, float am)
{
v1.X += am;
v1.Y += am;
v1.Z += am;
return v1;
}
public static Vertex operator -(Vertex v1, float am)
{
v1.X -= am;
v1.Y -= am;
v1.Z -= am;
return v1;
}
public static Vertex operator *(Vertex v1, float am)
{
v1.X *= am;
v1.Y *= am;
v1.Z *= am;
return v1;
}
public static Vertex operator /(Vertex v1, float am)
{
if (am == 0f)
{
return new Vertex(0f,0f,0f);
}
float mul = 1.0f / am;
v1.X *= mul;
v1.Y *= mul;
v1.Z *= mul;
return v1;
}
#pragma warning restore 0108
public float dot(Vertex v)
{
return X * v.X + Y * v.Y + Z * v.Z;
}
public Vertex(Vector3 v)
{
vector = v;
}
public Vertex Clone()
{
return new Vertex(X, Y, Z);
}
public static Vertex FromAngle(double angle)
{
return new Vertex((float) Math.Cos(angle), (float) Math.Sin(angle), 0.0f);
}
public float Length()
{
return vector.Length();
}
public virtual bool Equals(Vertex v, float tolerance)
{
Vertex diff = this - v;
float d = diff.Length();
if (d < tolerance)
return true;
return false;
}
public int CompareTo(Vertex other)
{
if (X < other.X)
return -1;
if (X > other.X)
return 1;
if (Y < other.Y)
return -1;
if (Y > other.Y)
return 1;
if (Z < other.Z)
return -1;
if (Z > other.Z)
return 1;
return 0;
}
public static bool operator >(Vertex me, Vertex other)
{
return me.CompareTo(other) > 0;
}
public static bool operator <(Vertex me, Vertex other)
{
return me.CompareTo(other) < 0;
}
public String ToRaw()
{
// Why this stuff with the number formatter?
// Well, the raw format uses the english/US notation of numbers
// where the "," separates groups of 1000 while the "." marks the border between 1 and 10E-1.
// The german notation uses these characters exactly vice versa!
// The Float.ToString() routine is a localized one, giving different results depending on the country
// settings your machine works with. Unusable for a machine readable file format :-(
NumberFormatInfo nfi = new NumberFormatInfo();
nfi.NumberDecimalSeparator = ".";
nfi.NumberDecimalDigits = 3;
String s1 = X.ToString("N2", nfi) + " " + Y.ToString("N2", nfi) + " " + Z.ToString("N2", nfi);
return s1;
}
}
public class Triangle
{
public Vertex v1;
public Vertex v2;
public Vertex v3;
private float radius_square;
private float cx;
private float cy;
public Triangle(Vertex _v1, Vertex _v2, Vertex _v3)
{
v1 = _v1;
v2 = _v2;
v3 = _v3;
CalcCircle();
}
public bool isInCircle(float x, float y)
{
float dx, dy;
float dd;
dx = x - cx;
dy = y - cy;
dd = dx*dx + dy*dy;
if (dd < radius_square)
return true;
else
return false;
}
public bool isDegraded()
{
// This means, the vertices of this triangle are somewhat strange.
// They either line up or at least two of them are identical
return (radius_square == 0.0);
}
private void CalcCircle()
{
// Calculate the center and the radius of a circle given by three points p1, p2, p3
// It is assumed, that the triangles vertices are already set correctly
double p1x, p2x, p1y, p2y, p3x, p3y;
// Deviation of this routine:
// A circle has the general equation (M-p)^2=r^2, where M and p are vectors
// this gives us three equations f(p)=r^2, each for one point p1, p2, p3
// putting respectively two equations together gives two equations
// f(p1)=f(p2) and f(p1)=f(p3)
// bringing all constant terms to one side brings them to the form
// M*v1=c1 resp.M*v2=c2 where v1=(p1-p2) and v2=(p1-p3) (still vectors)
// and c1, c2 are scalars (Naming conventions like the variables below)
// Now using the equations that are formed by the components of the vectors
// and isolate Mx lets you make one equation that only holds My
// The rest is straight forward and eaasy :-)
//
/* helping variables for temporary results */
double c1, c2;
double v1x, v1y, v2x, v2y;
double z, n;
double rx, ry;
// Readout the three points, the triangle consists of
p1x = v1.X;
p1y = v1.Y;
p2x = v2.X;
p2y = v2.Y;
p3x = v3.X;
p3y = v3.Y;
/* calc helping values first */
c1 = (p1x*p1x + p1y*p1y - p2x*p2x - p2y*p2y)/2;
c2 = (p1x*p1x + p1y*p1y - p3x*p3x - p3y*p3y)/2;
v1x = p1x - p2x;
v1y = p1y - p2y;
v2x = p1x - p3x;
v2y = p1y - p3y;
z = (c1*v2x - c2*v1x);
n = (v1y*v2x - v2y*v1x);
if (n == 0.0) // This is no triangle, i.e there are (at least) two points at the same location
{
radius_square = 0.0f;
return;
}
cy = (float) (z/n);
if (v2x != 0.0)
{
cx = (float) ((c2 - v2y*cy)/v2x);
}
else if (v1x != 0.0)
{
cx = (float) ((c1 - v1y*cy)/v1x);
}
else
{
Debug.Assert(false, "Malformed triangle"); /* Both terms zero means nothing good */
}
rx = (p1x - cx);
ry = (p1y - cy);
radius_square = (float) (rx*rx + ry*ry);
}
public override String ToString()
{
NumberFormatInfo nfi = new NumberFormatInfo();
nfi.CurrencyDecimalDigits = 2;
nfi.CurrencyDecimalSeparator = ".";
String s1 = "<" + v1.X.ToString(nfi) + "," + v1.Y.ToString(nfi) + "," + v1.Z.ToString(nfi) + ">";
String s2 = "<" + v2.X.ToString(nfi) + "," + v2.Y.ToString(nfi) + "," + v2.Z.ToString(nfi) + ">";
String s3 = "<" + v3.X.ToString(nfi) + "," + v3.Y.ToString(nfi) + "," + v3.Z.ToString(nfi) + ">";
return s1 + ";" + s2 + ";" + s3;
}
public Vector3 getNormal()
{
// Vertices
// Vectors for edges
Vector3 e1;
Vector3 e2;
e1 = new Vector3(v1.X - v2.X, v1.Y - v2.Y, v1.Z - v2.Z);
e2 = new Vector3(v1.X - v3.X, v1.Y - v3.Y, v1.Z - v3.Z);
// Cross product for normal
Vector3 n = Vector3.Cross(e1, e2);
// Length
float l = n.Length();
// Normalized "normal"
n = n/l;
return n;
}
public void invertNormal()
{
Vertex vt;
vt = v1;
v1 = v2;
v2 = vt;
}
// Dumps a triangle in the "raw faces" format, blender can import. This is for visualisation and
// debugging purposes
public String ToStringRaw()
{
String output = v1.ToRaw() + " " + v2.ToRaw() + " " + v3.ToRaw();
return output;
}
}