org.jcae.mesh.amibe.metrics
Class Quadric3DError

java.lang.Object
  org.jcae.mesh.amibe.metrics.Quadric3DError

All Implemented Interfaces:

java.io.Serializable

public class Quadric3DError
extends java.lang.Object
implements java.io.Serializable

Garland's Quadric Error Metric. See quadric error metrics.

A plane is fully determined by its normal N and the signed distance d of the frame origin to this plane, or in other words the equation of this plane is tN V + d = 0. The squared distance of a point to this plane is

   D*D = (tN V + d) * (tN V + d)
       = tV (N tN) V + 2d tN V + d*d
       = tV A V + 2 tB V + c
 

The quadric Q=(A,B,c)=(N tN, dN, d*d) is thus naturally defined. Addition of these quadrics have a simple form: Q1(V)+Q2(V)=(Q1+Q2)(V) with Q1+Q2=(A1+A2, B1+B2, c1+c2) To compute the squared distance of a point to a set of planes, we can then compute this quadric for each plane and sum each element of these quadrics.

When an edge (V1,V2) is contracted into V3, Q1(V3)+Q2(V3) represents the deviation to the set of planes at V1 and V2. The cost of this contraction is thus defined as Q1(V3)+Q2(V3). We want to minimize this error. It can be shown that if A is non singular, the optimal placement is for V3=-inv(A) B.

See Also:

Serialized Form

Nested Class Summary

static class

Quadric3DError.Placement

Constructor Summary

Quadric3DError()

Method Summary

void	addError(double[] normal, double d, double a)
void	computeQuadric3DError(Quadric3DError q1, Quadric3DError q2)
double	detA()
void	optimalPlacement(Vertex v1, Vertex v2, Quadric3DError q1, Quadric3DError q2, Quadric3DError.Placement p, Vertex ret)
java.lang.String	toString()
double	value(double[] vect)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Quadric3DError

public Quadric3DError()

Method Detail

computeQuadric3DError

public void computeQuadric3DError(Quadric3DError q1,
                                  Quadric3DError q2)

value

public double value(double[] vect)

addError

public void addError(double[] normal,
                     double d,
                     double a)

detA

public double detA()

optimalPlacement

public void optimalPlacement(Vertex v1,
                             Vertex v2,
                             Quadric3DError q1,
                             Quadric3DError q2,
                             Quadric3DError.Placement p,
                             Vertex ret)

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object