path: root/geometry.cpp

#include "geometry.h"
#include <math.h>
#include <stdlib.h>
#include <gtk/gtk.h>


void addVertex(VERTEX_LIST *list, const VERTEX *v) {
  list->nVertices++;
  list->vertices = (VERTEX*)realloc(list->vertices, list->nVertices*sizeof(VERTEX));
  list->vertices[list->nVertices-1] = *v;
}

void insertVertex(VERTEX_LIST *list, const VERTEX *v, unsigned int n) {
  int i;
  
  if(n > list->nVertices)
    n = list->nVertices;
  
  list->nVertices++;
  list->vertices = (VERTEX*)realloc(list->vertices, list->nVertices*sizeof(VERTEX));
  
  for(i = list->nVertices-1; i > n; i--)
    list->vertices[i] = list->vertices[i-1];
  
  list->vertices[n] = *v;
}

void deleteVertex(VERTEX_LIST *list, unsigned int n) {
  int i;
  
  list->nVertices--;
  
  for(i = n; i < list->nVertices; i++)
    list->vertices[i] = list->vertices[i+1];
  
  list->vertices = (VERTEX*)realloc(list->vertices, list->nVertices*sizeof(VERTEX));
}

double vertexDistanceSquare(const VERTEX *v1, const VERTEX *v2) {
  return (v1->x-v2->x)*(v1->x-v2->x) + (v1->y-v2->y)*(v1->y-v2->y);
}

double vertexDistance(const VERTEX *v1, const VERTEX *v2) {
  return sqrt(vertexDistanceSquare(v1, v2));
}

int vertexOnLine(const VERTEX *v, const LINE *l) {
  if(l->v1.x == l->v2.x && l->v1.y == l->v2.y) {
    if(l->v1.x == v->x && l->v1.y == v->y) return 1;
    else return 0;
  }
  
  if(l->v1.x == l->v2.x) {
    if(l->v1.x != v->x) return 0;
    else if(v->y >= MIN(l->v1.y, l->v2.y) && v->y <= MAX(l->v1.y, l->v2.y)) return 1;
    else return 1;
  }
  
  if(l->v1.y == l->v2.y) {
    if(l->v1.y != v->y) return 0;
    else if(v->x >= MIN(l->v1.x, l->v2.x) && v->x <= MAX(l->v1.x, l->v2.x)) return 1;
    else return 1;
  }
  if((v->x-l->v1.x)/(l->v2.x-l->v1.x) - (v->y-l->v1.y)/(l->v2.y-l->v1.y) == 0) return 1;
  else return 0;
}

int vertexInRect(const VERTEX *v, const RECTANGLE *rect) {
  int ret = EDGE_NONE;
  
  if(v->x < rect->x) ret |= EDGE_LEFT;
  else if(v->x >= rect->x+rect->width) ret |= EDGE_RIGHT;
  
  if(v->y < rect->y) ret |= EDGE_TOP;
  else if(v->y >= rect->y+rect->height) ret |= EDGE_BOTTOM;
  
  return ret;
}

static int quadrant(VERTEX *v) {
  if(v->x > 0 && v->y >= 0) return 1;
  if(v->x >= 0 && v->y < 0) return 2;
  if(v->x < 0 && v->y <= 0) return 3;
  if(v->x <= 0 && v->y > 0) return 4;
  
  return 0;
}

gboolean vertexInPolygon(const VERTEX *v, const POLYGON *p) {
  int d = 0, i, li;
  int q, ql, q2;
  LINE d1 = {{-1, -1}, {1, 1}};
  LINE d2 = {{-1, 1}, {1, -1}};
  LINE l;
  VERTEX v2;
  
  
  if(p->nVertices == 0) return FALSE;
  
  v2.x = p->vertices[p->nVertices-1].x - v->x;
  v2.y = p->vertices[p->nVertices-1].y - v->y;
  q = quadrant(&v2);
  
  if(q == 0) return TRUE;
  
  for(i = 0; i < p->nVertices; i++) {
    ql = q;
    
    v2.x = p->vertices[i].x - v->x;
    v2.y = p->vertices[i].y - v->y;
    q = quadrant(&v2);
    
    if(q == 0) return TRUE;
    
    switch(q-ql) {
      case 0:
        break;
      case 1:
      case -3:
        d++;
        break;
      case 3:
      case -1:
        d--;
        break;
      default:
        l.v1.x = p->vertices[(i>0)?i-1:p->nVertices-1].x - v->x;
        l.v1.y = p->vertices[(i>0)?i-1:p->nVertices-1].y - v->y;
        
        l.v2 = v2;
        
        if(q == 1 || q == 3) {
          if(!(lineIntersection(&l, &d2, &v2) & INTERSECTION_LINE)) return FALSE;
          
          q2 = quadrant(&v2);
          if(q2 == 0) return TRUE;
          
          if((q == 1 && q2 == 2) || (q == 3 && q2 == 4)) d -= 2;
          else d += 2;
        }
        else {
          if(!(lineIntersection(&l, &d1, &v2) & INTERSECTION_LINE)) return FALSE;
          
          q2 = quadrant(&v2);
          if(q2 == 0) return TRUE;
          
          if((q == 2 && q2 == 3) || (q == 4 && q2 == 1)) d -= 2;
          else d += 2;
        }
    }
  }
  
  return (d == 0) ? FALSE : TRUE;
}

double polygonPerimeter(const POLYGON *p) {
  int i;
  double d = 0.0;
  
  for(i = 0; i < p->nVertices; i++)
    d += vertexDistance(&p->vertices[i], &p->vertices[(i+1)%p->nVertices]);
  
  return d;
}

double polygonArea(const POLYGON *p) {
  int i;
  double d = 0.0;
  
  for(i = 0; i < p->nVertices; i++)
    d += (p->vertices[(i+1)%p->nVertices].x+p->vertices[i].x)*(p->vertices[(i+1)%p->nVertices].y-p->vertices[i].y);
  
  return fabs(d/2);
}

int lineIntersection(const LINE *la, const LINE *lb, VERTEX *v) {
  double xa1 = la->v1.x, ya1 = la->v1.y;
  double xa2 = la->v2.x, ya2 = la->v2.y;
  double xb1 = lb->v1.x, yb1 = lb->v1.y;
  double xb2 = lb->v2.x, yb2 = lb->v2.y;
  double temp;
  int switched = 0;
  VERTEX v2;
  
  
  if(v == NULL) v = &v2;
  
  if(xa1 == xa2 && ya1 == ya2) return INTERSECTION_ERROR;
  if(xb1 == xb2 && yb1 == yb2) return INTERSECTION_ERROR;
  
  if(xa1 == xa2 || xb1 == xb2) {
    temp = xa1; xa1 = ya1; ya1 = temp;
    temp = xa2; xa2 = ya2; ya2 = temp;
    temp = xb1; xb1 = yb1; yb1 = temp;
    temp = xb2; xb2 = yb2; yb2 = temp;
    
    switched = 1;
  }
  
  if(xa1 == xa2 && xb1 == xb2)
    return (xa1 == xb1) ? INTERSECTION_IDENTICAL : INTERSECTION_NONE;
  
  if(xa1 == xa2) {
    v->x = xa1;
    v->y = yb1;
  }
  else if(xb1 == xb2) {
    v->x = xb1;
    v->y = ya1;
  }
  else {
    double ma = (ya2-ya1)/(xa2-xa1);
    double mb = (yb2-yb1)/(xb2-xb1);
    double ba = ya1 - ma*xa1;
    double bb = yb1 - mb*xb1;
    
    if(ma == mb) return (ba == bb) ? INTERSECTION_IDENTICAL : INTERSECTION_NONE;
    
    v->x = (bb-ba)/(ma-mb);
    v->y = ma*v->x + ba;
  }
  
  if(switched) {
    temp = v->x; v->x = v->y; v->y = temp;
    
    //switch back everything for segment tests
    temp = xa1; xa1 = ya1; ya1 = temp;
    temp = xa2; xa2 = ya2; ya2 = temp;
    temp = xb1; xb1 = yb1; yb1 = temp;
    temp = xb2; xb2 = yb2; yb2 = temp;
  }
  
  if(v->x < MIN(xa1,xa2) || v->x > MAX(xa1, xa2) || v->y < MIN(ya1,ya2) || v->y > MAX(ya1, ya2)) {
    if(v->x < MIN(xb1,xb2) || v->x > MAX(xb1, xb2) || v->y < MIN(yb1,yb2) || v->y > MAX(yb1, yb2))
      return INTERSECTION_LINE_LINE;
    else
      return INTERSECTION_LINE_SEGMENT;
  }
  else if(v->x < MIN(xb1,xb2) || v->x > MAX(xb1, xb2) || v->y < MIN(yb1,yb2) || v->y > MAX(yb1, yb2))
    return INTERSECTION_SEGMENT_LINE;
  else
    return INTERSECTION_SEGMENT_SEGMENT;
}

int lineRectIntersection(const LINE *l, const RECTANGLE *rect, int edge, VERTEX *v) {
  const double minX = rect->x, maxX = rect->x+rect->width;
  const double minY = rect->y, maxY = rect->y+rect->height;
  const LINE top = {{minX, minY}, {maxX, minY}};
  const LINE bottom = {{minX, maxY}, {maxX, maxY}};
  const LINE left = {{minX, minY}, {minX, maxY}};
  const LINE right = {{maxX, minY}, {maxX, maxY}};
  
  if((edge & EDGE_TOP) && (lineIntersection(&top, l, v) == INTERSECTION_SEGMENT_SEGMENT))
    return EDGE_TOP;
  if((edge & EDGE_BOTTOM) && (lineIntersection(&bottom, l, v) == INTERSECTION_SEGMENT_SEGMENT))
    return EDGE_BOTTOM;
  if((edge & EDGE_LEFT) && (lineIntersection(&left, l, v) == INTERSECTION_SEGMENT_SEGMENT))
    return EDGE_LEFT;
  if((edge & EDGE_RIGHT) && (lineIntersection(&right, l, v) == INTERSECTION_SEGMENT_SEGMENT))
    return EDGE_RIGHT;
  
  v->x = v->y = 0;
  
  return EDGE_NONE;
}

int lineRectIntersections(const LINE *line, const RECTANGLE *rect, int edge, VERTEX *v1, VERTEX *v2) {
  int ret = EDGE_NONE;
  
  ret |= lineRectIntersection(line, rect, edge, v1);
  ret |= lineRectIntersection(line, rect, EDGE_ALL^edge, v2);
  
  return ret;
}

gboolean linePolygonIntersection(const LINE *l, const POLYGON *p) {
  int i;
  LINE line;
  
  for(i = 0; i < p->nVertices; i++) {
    line.v1 = p->vertices[i];
    line.v2 = p->vertices[(i+1)%p->nVertices];
    
    if(lineIntersection(l, &line, NULL) == INTERSECTION_SEGMENT_SEGMENT)
      return TRUE;
  }
  
  return FALSE;
}


static void edgeVertex(VERTEX *v, int edge, const RECTANGLE *rect) {
  if(edge == EDGE_NONE)
    edge = vertexInRect(v, rect);
  
  if(edge & EDGE_LEFT) v->x = rect->x;
  else if(edge & EDGE_RIGHT) v->x = rect->x+rect->width;
  
  if(edge & EDGE_TOP) v->y = rect->y;
  else if(edge & EDGE_BOTTOM) v->y = rect->y+rect->height;
}

static int simplifyVertex(VERTEX *v, const VERTEX *to, const RECTANGLE *rect) {
  LINE l = {*v, *to};
  int edge, edge2;
  
  
  edge = vertexInRect(v, rect);
  if(edge == EDGE_NONE) return EDGE_NONE;
  
  edge2 = lineRectIntersection(&l, rect, edge, v);
  if(edge2 != EDGE_NONE) return edge2;
  
  edgeVertex(v, edge, rect);
  return edge;
}



static void addSimplifiedLine(const VERTEX *v1, const VERTEX *v2, const RECTANGLE *rect, int last, POLYGON *out) {
  const LINE d1 = {{rect->x, rect->y}, {rect->x+rect->width, rect->y+rect->height}};
  const LINE d2 = {{rect->x, rect->y+rect->height}, {rect->x+rect->width, rect->y}};
  
  LINE l = {*v1, *v2};
  VERTEX v, vi;
  int edge1, edge2;
  
  
  v = *v1;
  if((edge1 = simplifyVertex(&v, v2, rect)) != EDGE_NONE)
    addVertex(out, &v);
  
  v = *v2;
  edge2 = simplifyVertex(&v, v1, rect);
  
  if(edge1 != EDGE_NONE && edge2 != EDGE_NONE && !(edge1 & edge2)) {
    if(lineIntersection(&l, &d1, &vi) == INTERSECTION_SEGMENT_LINE) {
      edgeVertex(&vi, 0, rect);
      addVertex(out, &vi);
    }
    else if(lineIntersection(&l, &d2, &vi) == INTERSECTION_SEGMENT_LINE) {
      edgeVertex(&vi, 0, rect);
      addVertex(out, &vi);
    }
  }
  
  if(!last)
    addVertex(out, &v);
}

void simplifyPolygon(const POLYGON *in, const RECTANGLE *rect, POLYGON *out) {
  VERTEX v;
  int i;
  
  if(in->nVertices == 0) return;
  else if(in->nVertices == 1) {
    addVertex(out, &in->vertices[0]);
    return;
  }
  
  v = in->vertices[0];
  simplifyVertex(&v, &in->vertices[in->nVertices-1], rect);
  addVertex(out, &v);
  
  for(i = 0; i < in->nVertices; i++) {
    addSimplifiedLine(&in->vertices[i], &in->vertices[(i+1)%in->nVertices], rect, (i == in->nVertices-1), out);
  }
}