Initial work on progressive mesh generation. Currently based on Stan Melax's PolyChop.
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David Williams
314
library/PolyVoxCore/source/progmesh.cpp
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314
library/PolyVoxCore/source/progmesh.cpp
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/*
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* Progressive Mesh type Polygon Reduction Algorithm
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* by Stan Melax (c) 1998
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* Permission to use any of this code wherever you want is granted..
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* Although, please do acknowledge authorship if appropriate.
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*
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* See the header file progmesh.h for a description of this module
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*/
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#include <stdio.h>
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#include <math.h>
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#include <stdlib.h>
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#include <assert.h>
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#include <windows.h>
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#include <iostream>
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#include "vector_melax.h"
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#include "list.h"
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#include "progmesh.h"
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/*
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* For the polygon reduction algorithm we use data structures
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* that contain a little bit more information than the usual
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* indexed face set type of data structure.
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* From a vertex we wish to be able to quickly get the
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* neighboring faces and vertices.
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*/
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class Triangle;
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class Vertex;
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class Triangle {
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public:
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Vertex * vertex[3]; // the 3 points that make this tri
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VectorM normal; // unit vector othogonal to this face
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Triangle(Vertex *v0,Vertex *v1,Vertex *v2);
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~Triangle();
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void ComputeNormal();
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void ReplaceVertex(Vertex *vold,Vertex *vnew);
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int HasVertex(Vertex *v);
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};
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class Vertex {
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public:
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VectorM position; // location of point in euclidean space
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int id; // place of vertex in original list
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List<Vertex *> neighbor; // adjacent vertices
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List<Triangle *> face; // adjacent triangles
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float objdist; // cached cost of collapsing edge
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Vertex * collapse; // candidate vertex for collapse
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Vertex(VectorM v,int _id);
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~Vertex();
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void RemoveIfNonNeighbor(Vertex *n);
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};
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List<Vertex *> vertices;
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List<Triangle *> triangles;
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Triangle::Triangle(Vertex *v0,Vertex *v1,Vertex *v2){
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assert(v0!=v1 && v1!=v2 && v2!=v0);
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vertex[0]=v0;
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vertex[1]=v1;
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vertex[2]=v2;
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ComputeNormal();
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triangles.Add(this);
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for(int i=0;i<3;i++) {
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vertex[i]->face.Add(this);
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for(int j=0;j<3;j++) if(i!=j) {
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vertex[i]->neighbor.AddUnique(vertex[j]);
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}
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}
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}
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Triangle::~Triangle(){
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int i;
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triangles.Remove(this);
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for(i=0;i<3;i++) {
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if(vertex[i]) vertex[i]->face.Remove(this);
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}
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for(i=0;i<3;i++) {
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int i2 = (i+1)%3;
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if(!vertex[i] || !vertex[i2]) continue;
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vertex[i ]->RemoveIfNonNeighbor(vertex[i2]);
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vertex[i2]->RemoveIfNonNeighbor(vertex[i ]);
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}
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}
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int Triangle::HasVertex(Vertex *v) {
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return (v==vertex[0] ||v==vertex[1] || v==vertex[2]);
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}
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void Triangle::ComputeNormal(){
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VectorM v0=vertex[0]->position;
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VectorM v1=vertex[1]->position;
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VectorM v2=vertex[2]->position;
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normal = (v1-v0)*(v2-v1);
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if(magnitude(normal)==0)return;
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normal = normalize(normal);
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}
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void Triangle::ReplaceVertex(Vertex *vold,Vertex *vnew) {
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assert(vold && vnew);
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assert(vold==vertex[0] || vold==vertex[1] || vold==vertex[2]);
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assert(vnew!=vertex[0] && vnew!=vertex[1] && vnew!=vertex[2]);
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if(vold==vertex[0]){
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vertex[0]=vnew;
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}
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else if(vold==vertex[1]){
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vertex[1]=vnew;
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}
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else {
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assert(vold==vertex[2]);
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vertex[2]=vnew;
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}
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int i;
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vold->face.Remove(this);
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assert(!vnew->face.Contains(this));
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vnew->face.Add(this);
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for(i=0;i<3;i++) {
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vold->RemoveIfNonNeighbor(vertex[i]);
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vertex[i]->RemoveIfNonNeighbor(vold);
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}
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for(i=0;i<3;i++) {
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assert(vertex[i]->face.Contains(this)==1);
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for(int j=0;j<3;j++) if(i!=j) {
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vertex[i]->neighbor.AddUnique(vertex[j]);
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}
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}
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ComputeNormal();
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}
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Vertex::Vertex(VectorM v,int _id) {
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position =v;
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id=_id;
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vertices.Add(this);
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}
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Vertex::~Vertex(){
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assert(face.num==0);
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while(neighbor.num) {
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neighbor[0]->neighbor.Remove(this);
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neighbor.Remove(neighbor[0]);
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}
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vertices.Remove(this);
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}
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void Vertex::RemoveIfNonNeighbor(Vertex *n) {
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// removes n from neighbor list if n isn't a neighbor.
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if(!neighbor.Contains(n)) return;
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for(int i=0;i<face.num;i++) {
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if(face[i]->HasVertex(n)) return;
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}
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neighbor.Remove(n);
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}
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float ComputeEdgeCollapseCost(Vertex *u,Vertex *v) {
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// if we collapse edge uv by moving u to v then how
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// much different will the model change, i.e. how much "error".
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// Texture, vertex normal, and border vertex code was removed
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// to keep this demo as simple as possible.
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// The method of determining cost was designed in order
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// to exploit small and coplanar regions for
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// effective polygon reduction.
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// Is is possible to add some checks here to see if "folds"
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// would be generated. i.e. normal of a remaining face gets
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// flipped. I never seemed to run into this problem and
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// therefore never added code to detect this case.
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int i;
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float edgelength = magnitude(v->position - u->position);
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float curvature=0;
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// find the "sides" triangles that are on the edge uv
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List<Triangle *> sides;
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for(i=0;i<u->face.num;i++) {
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if(u->face[i]->HasVertex(v)){
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sides.Add(u->face[i]);
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}
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}
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// use the triangle facing most away from the sides
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// to determine our curvature term
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for(i=0;i<u->face.num;i++) {
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float mincurv=1; // curve for face i and closer side to it
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for(int j=0;j<sides.num;j++) {
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// use dot product of face normals. '^' defined in vector
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float dotprod = u->face[i]->normal ^ sides[j]->normal;
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mincurv = min(mincurv,(1-dotprod)/2.0f);
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}
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curvature = max(curvature,mincurv);
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}
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float boundaryCost = u->position.fBoundaryCost + v->position.fBoundaryCost;
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// the more coplanar the lower the curvature term
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return edgelength * curvature + boundaryCost;
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}
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void ComputeEdgeCostAtVertex(Vertex *v) {
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// compute the edge collapse cost for all edges that start
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// from vertex v. Since we are only interested in reducing
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// the object by selecting the min cost edge at each step, we
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// only cache the cost of the least cost edge at this vertex
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// (in member variable collapse) as well as the value of the
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// cost (in member variable objdist).
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if(v->neighbor.num==0) {
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// v doesn't have neighbors so it costs nothing to collapse
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v->collapse=NULL;
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v->objdist=-0.01f;
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return;
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}
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v->objdist = 1000000;
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v->collapse=NULL;
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// search all neighboring edges for "least cost" edge
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for(int i=0;i<v->neighbor.num;i++) {
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float dist;
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dist = ComputeEdgeCollapseCost(v,v->neighbor[i]);
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//std::cout << "Cost: " << dist << std::endl;
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if(dist<v->objdist) {
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v->collapse=v->neighbor[i]; // candidate for edge collapse
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v->objdist=dist; // cost of the collapse
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}
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}
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}
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void ComputeAllEdgeCollapseCosts() {
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// For all the edges, compute the difference it would make
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// to the model if it was collapsed. The least of these
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// per vertex is cached in each vertex object.
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for(int i=0;i<vertices.num;i++) {
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ComputeEdgeCostAtVertex(vertices[i]);
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}
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}
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void Collapse(Vertex *u,Vertex *v){
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// Collapse the edge uv by moving vertex u onto v
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// Actually remove tris on uv, then update tris that
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// have u to have v, and then remove u.
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if(!v) {
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// u is a vertex all by itself so just delete it
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delete u;
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return;
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}
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int i;
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List<Vertex *>tmp;
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// make tmp a list of all the neighbors of u
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for(i=0;i<u->neighbor.num;i++) {
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tmp.Add(u->neighbor[i]);
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}
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// delete triangles on edge uv:
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for(i=u->face.num-1;i>=0;i--) {
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if(u->face[i]->HasVertex(v)) {
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delete(u->face[i]);
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}
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}
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// update remaining triangles to have v instead of u
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for(i=u->face.num-1;i>=0;i--) {
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u->face[i]->ReplaceVertex(u,v);
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}
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delete u;
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// recompute the edge collapse costs for neighboring vertices
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for(i=0;i<tmp.num;i++) {
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ComputeEdgeCostAtVertex(tmp[i]);
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}
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}
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void AddVertex(List<VectorM> &vert){
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for(int i=0;i<vert.num;i++) {
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Vertex *v = new Vertex(vert[i],i);
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}
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}
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void AddFaces(List<tridata> &tri){
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for(int i=0;i<tri.num;i++) {
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Triangle *t=new Triangle(
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vertices[tri[i].v[0]],
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vertices[tri[i].v[1]],
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vertices[tri[i].v[2]] );
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}
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}
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Vertex *MinimumCostEdge(){
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// Find the edge that when collapsed will affect model the least.
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// This funtion actually returns a Vertex, the second vertex
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// of the edge (collapse candidate) is stored in the vertex data.
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// Serious optimization opportunity here: this function currently
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// does a sequential search through an unsorted list :-(
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// Our algorithm could be O(n*lg(n)) instead of O(n*n)
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Vertex *mn=vertices[0];
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for(int i=0;i<vertices.num;i++) {
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if(vertices[i]->objdist < mn->objdist) {
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mn = vertices[i];
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}
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}
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return mn;
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}
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void ProgressiveMesh(List<VectorM> &vert, List<tridata> &tri,
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List<int> &map, List<int> &permutation)
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{
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AddVertex(vert); // put input data into our data structures
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AddFaces(tri);
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ComputeAllEdgeCollapseCosts(); // cache all edge collapse costs
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permutation.SetSize(vertices.num); // allocate space
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map.SetSize(vertices.num); // allocate space
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// reduce the object down to nothing:
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while(vertices.num > 0) {
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// get the next vertex to collapse
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Vertex *mn = MinimumCostEdge();
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// keep track of this vertex, i.e. the collapse ordering
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permutation[mn->id]=vertices.num-1;
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// keep track of vertex to which we collapse to
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map[vertices.num-1] = (mn->collapse)?mn->collapse->id:-1;
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// Collapse this edge
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Collapse(mn,mn->collapse);
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}
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// reorder the map list based on the collapse ordering
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for(int i=0;i<map.num;i++) {
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map[i] = (map[i]==-1)?0:permutation[map[i]];
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}
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// The caller of this function should reorder their vertices
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// according to the returned "permutation".
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}
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