/*---------------------------------------------------------------------
'p': The segment lies wholly within the plane.
'q': The q endpoint is on the plane (but not 'p').
'r': The r endpoint is on the plane (but not 'p').
'0': The segment lies strictly to one side or the other of the plane.
'1': The segement intersects the plane, and 'p' does not hold.
---------------------------------------------------------------------*/
char SegPlaneInt( tPointi T, tPointd q, tPointd r, tPointd p, int *m)
{
tPointd N; double d;
tPointd rq;
double num, denom, t;
int i;
*m = PlaneCoeff( T, N, &d );
/*printf("m=%d; plane=(%lf,%lf,%lf,%lf)\n", m, N[X],N[Y],N[Z],d);*/
num = d - Dot( q, N );
SubVec( r, q, rq );
denom = Dot( rq, N );
/*printf("SegPlaneInt: num=%lf, denom=%lf\n", num, denom );*/
if ( denom == 0.0 ) { /* Segment is parallel to plane. */
if ( num == 0.0 ) /* q is on plane. */
return 'p';
else
return '0';
}
else
t = num / denom;
/*printf("SegPlaneInt: t=%lf \n", t );*/
for( i = 0; i < DIM; i++ )
p[i] = q[i] + t * ( r[i] - q[i] );
if ( (0.0 < t) && (t < 1.0) )
return '1';
else if ( num == 0.0 ) /* t == 0 */
return 'q';
else if ( num == denom ) /* t == 1 */
return 'r';
else return '0';
}
/*---------------------------------------------------------------------
---------------------------------------------------------------------*/
void ConvexIntersect( tPolygoni P, tPolygoni Q, int n, int m )
/* P has n vertices, Q has m vertices. */
{
int a, b; /* indices on P and Q (resp.) */
int a1, b1; /* a-1, b-1 (resp.) */
tPointi A, B; /* directed edges on P and Q (resp.) */
int cross; /* sign of z-component of A x B */
int bHA, aHB; /* b in H(A); a in H(b). */
tPointi Origin = {0,0}; /* (0,0) */
tPointd p; /* double point of intersection */
tPointd q; /* second point of intersection */
tInFlag inflag; /* {Pin, Qin, Unknown}: which inside */
int aa, ba; /* # advances on a & b indices (after 1st inter.) */
bool FirstPoint; /* Is this the first point? (used to initialize).*/
tPointd p0; /* The first point. */
int code; /* SegSegInt return code. */
/* Initialize variables. */
a = 0; b = 0; aa = 0; ba = 0;
inflag = Unknown; FirstPoint = TRUE;
do {
/*printf("%%Before Advances:a=%d, b=%d; aa=%d, ba=%d; inflag=%d\n", a, b, aa, ba, inflag);*/
/* Computations of key variables. */
a1 = (a + n - 1) % n;
b1 = (b + m - 1) % m;
SubVec( P[a], P[a1], A );
SubVec( Q[b], Q[b1], B );
cross = AreaSign( Origin, A, B );
aHB = AreaSign( Q[b1], Q[b], P[a] );
bHA = AreaSign( P[a1], P[a], Q[b] );
printf("%%cross=%d, aHB=%d, bHA=%d\n", cross, aHB, bHA );
/* If A & B intersect, update inflag. */
code = SegSegInt( P[a1], P[a], Q[b1], Q[b], p, q );
printf("%%SegSegInt: code = %c\n", code );
if ( code == '1' || code == 'v' ) {
if ( inflag == Unknown && FirstPoint ) {
aa = ba = 0;
FirstPoint = FALSE;
p0[X] = p[X]; p0[Y] = p[Y];
printf("%8.2lf %8.2lf moveto\n", p0[X], p0[Y] );
}
inflag = InOut( p, inflag, aHB, bHA );
printf("%%InOut sets inflag=%d\n", inflag);
}
/*-----Advance rules-----*/
/* Special case: A & B overlap and oppositely oriented. */
if ( ( code == 'e' ) && (Dot( A, B ) < 0) )
PrintSharedSeg( p, q ), exit(EXIT_SUCCESS);
/* Special case: A & B parallel and separated. */
if ( (cross == 0) && ( aHB < 0) && ( bHA < 0 ) )
printf("%%P and Q are disjoint.\n"), exit(EXIT_SUCCESS);
/* Special case: A & B collinear. */
else if ( (cross == 0) && ( aHB == 0) && ( bHA == 0 ) ) {
/* Advance but do not output point. */
if ( inflag == Pin )
b = Advance( b, &ba, m, inflag == Qin, Q[b] );
else
a = Advance( a, &aa, n, inflag == Pin, P[a] );
}
/* Generic cases. */
else if ( cross >= 0 ) {
if ( bHA > 0)
a = Advance( a, &aa, n, inflag == Pin, P[a] );
else
b = Advance( b, &ba, m, inflag == Qin, Q[b] );
}
else /* if ( cross < 0 ) */{
if ( aHB > 0)
b = Advance( b, &ba, m, inflag == Qin, Q[b] );
else
a = Advance( a, &aa, n, inflag == Pin, P[a] );
}
printf("%%After advances:a=%d, b=%d; aa=%d, ba=%d; inflag=%d\n", a, b, aa, ba, inflag);
/* Quit when both adv. indices have cycled, or one has cycled twice. */
} while ( ((aa < n) || (ba < m)) && (aa < 2*n) && (ba < 2*m) );
if ( !FirstPoint ) /* If at least one point output, close up. */
printf("%8.2lf %8.2lf lineto\n", p0[X], p0[Y] );
/* Deal with special cases: not implemented. */
if ( inflag == Unknown)
printf("%%The boundaries of P and Q do not cross.\n");
}
/*---------------------------------------------------------------------
Print: Prints out the vertices and the faces. Uses the vnum indices
corresponding to the order in which the vertices were input.
Output is in PostScript format.
---------------------------------------------------------------------*/
void Print( void )
{
/* Pointers to vertices, edges, faces. */
tVertex v;
tEdge e;
tFace f;
int xmin, ymin, xmax, ymax;
int a[3], b[3]; /* used to compute normal vector */
/* Counters for Euler's formula. */
int V = 0, E = 0 , F = 0;
/* Note: lowercase==pointer, uppercase==counter. */
/*-- find X min & max --*/
v = vertices;
xmin = xmax = v->v[X];
do {
if( v->v[X] > xmax ) xmax = v->v[X];
else
if( v->v[X] < xmin ) xmin = v->v[X];
v = v->next;
} while ( v != vertices );
/*-- find Y min & max --*/
v = vertices;
ymin = ymax = v->v[Y];
do {
if( v->v[Y] > ymax ) ymax = v->v[Y];
else
if( v->v[Y] < ymin ) ymin = v->v[Y];
v = v->next;
} while ( v != vertices );
/* PostScript header */
printf("%%!PS\n");
printf("%%%%BoundingBox: %d %d %d %d\n",
xmin, ymin, xmax, ymax);
printf(".00 .00 setlinewidth\n");
printf("%d %d translate\n", -xmin+72, -ymin+72 );
/* The +72 shifts the figure one inch from the lower left corner */
/* Vertices. */
v = vertices;
do {
if( v->mark ) V++;
v = v->next;
} while ( v != vertices );
printf("\n%%%% Vertices:\tV = %d\n", V);
printf("%%%% index:\tx\ty\tz\n");
do {
printf( "%%%% %5d:\t%d\t%d\t%d\n",
v->vnum, v->v[X], v->v[Y], v->v[Z] );
v = v->next;
} while ( v != vertices );
/* Faces. */
/* visible faces are printed as PS output */
f = faces;
do {
++F;
f = f ->next;
} while ( f != faces );
printf("\n%%%% Faces:\tF = %d\n", F );
printf("%%%% Visible faces only: \n");
do {
/* Print face only if it is visible: if normal vector >= 0 */
SubVec( f->vertex[1]->v, f->vertex[0]->v, a );
SubVec( f->vertex[2]->v, f->vertex[1]->v, b );
if(( a[0] * b[1] - a[1] * b[0] ) >= 0 )
{
printf("%%%% vnums: %d %d %d\n",
f->vertex[0]->vnum,
f->vertex[1]->vnum,
f->vertex[2]->vnum);
printf("newpath\n");
printf("%d\t%d\tmoveto\n",
f->vertex[0]->v[X], f->vertex[0]->v[Y] );
printf("%d\t%d\tlineto\n",
f->vertex[1]->v[X], f->vertex[1]->v[Y] );
printf("%d\t%d\tlineto\n",
f->vertex[2]->v[X], f->vertex[2]->v[Y] );
printf("closepath stroke\n\n");
}
f = f->next;
} while ( f != faces );
/* prints a list of all faces */
printf("%%%% List of all faces: \n");
printf("%%%%\tv0\tv1\tv2\t(vertex indices)\n");
do {
printf("%%%%\t%d\t%d\t%d\n",
f->vertex[0]->vnum,
f->vertex[1]->vnum,
f->vertex[2]->vnum );
f = f->next;
} while ( f != faces );
/* Edges. */
e = edges;
do {
E++;
e = e->next;
} while ( e != edges );
printf("\n%%%% Edges:\tE = %d\n", E );
/* Edges not printed out (but easily added). */
printf("\nshowpage\n\n");
check = TRUE;
CheckEuler( V, E, F );
}
