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/*
* intersect.c
* Find intersections of objects based on segment-plane intersections
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "CNdata.h"
#include "CNproperty.h"
#include "CNdatatypes.h"
#include "CNintersect.h"
/*
static void test_rect_intsct();
static void test_tria_intsct();
static void test_line_intsct();
main()
{
test_rect_intsct();
}
static void test_rect_intsct()
{
CNpoint pta, ptb, ptc, ptd;
CNpoint points[10];
int npts;
double a, b, c, d;
int intsct, i;
pta.x = 0.0; pta.y = 0.0; pta.z = 1.0;
ptb.x = 1.0; ptb.y = 0.0; ptb.z = 0.0;
ptc.x = 1.0; ptc.y = 1.0; ptc.z = 1.0;
ptd.x = 0.0; ptd.y = 1.0; ptd.z = 0.0;
(void) fprintf(stdout,"\nEnter the equation of the plane: (ax+by+cz=d)\n");
(void) fprintf(stdout," a ="); scanf("%lf",&a);
(void) fprintf(stdout," b ="); scanf("%lf",&b);
(void) fprintf(stdout," c ="); scanf("%lf",&c);
(void) fprintf(stdout," d ="); scanf("%lf",&d); d = -1.0*d;
(void) fprintf(stdout,"The plane equation is : %g*x + %g*y + %g*z = %g\n",a,b,c,-d);
intsct = CNpoly4_intsct_plane(a, b, c, d, &pta, &ptb, &ptc, &ptd,
points, &npts, 1);
(void) fprintf(stdout,"\nNo of intersections = %d No of segment pairs = %d\n",npts,npts/2);
for (i=0; i<npts; i++)
(void) fprintf(stdout,"pt %d = (%10.5f %10.5f %10.5f)\n",
i, points[i].x, points[i].y, points[i].z);
}
static void test_tria_intsct()
{
CNpoint pta, ptb, ptc;
CNpoint pt1, pt2;
double a, b, c, d;
int intsct;
pta.x = 0.0; pta.y = 0.0; pta.z = 1.0;
ptb.x = 1.0; ptb.y = 0.0; ptb.z = 1.0;
ptc.x = 1.0; ptc.y = 1.0; ptc.z = 1.0;
(void) fprintf(stdout,"\nEnter the equation of the plane: (ax+by+cz=d)\n");
(void) fprintf(stdout," a ="); scanf("%lf",&a);
(void) fprintf(stdout," b ="); scanf("%lf",&b);
(void) fprintf(stdout," c ="); scanf("%lf",&c);
(void) fprintf(stdout," d ="); scanf("%lf",&d); d = -1.0*d;
(void) fprintf(stdout,"The plane equation is : %g*x + %g*y + %g*z = %g\n",a,b,c,-d);
intsct = CNpoly3_intsct_plane(a, b, c, d, &pta, &ptb, &ptc, &pt1, &pt2, 1);
if (intsct) {
(void) fprintf(stdout,"Found intersection\n");
(void) fprintf(stdout,"pt1 = (%10.5f %10.5f %10.5f)\n", pt1.x, pt1.y, pt1.z);
(void) fprintf(stdout,"pt2 = (%10.5f %10.5f %10.5f)\n", pt2.x, pt2.y, pt2.z);
}
}
static void test_line_intsct()
{
CNpoint pta, ptb, ptc;
double a, b, c, d;
int intsct;
pta.x = 1.0; pta.y = 1.0; pta.z = 1.0;
ptb.x = 0.0; ptb.y = 0.0; ptb.z = 0.0;
ptc.x = 0.0; ptc.y = 0.0; ptc.z = 0.0;
(void) fprintf(stdout,"\nEnter the equation of the plane: (ax+by+cz=d)\n");
(void) fprintf(stdout," a ="); scanf("%lf",&a);
(void) fprintf(stdout," b ="); scanf("%lf",&b);
(void) fprintf(stdout," c ="); scanf("%lf",&c);
(void) fprintf(stdout," d ="); scanf("%lf",&d);
(void) fprintf(stdout,"The plane equation is : %g*x + %g*y + %g*z = %g\n",a,b,c,d);
intsct = CNline_intsct_plane(a, b, c, -d, &pta, &ptb, &ptc);
(void) fprintf(stdout,"pta = (%10.5f %10.5f %10.5f)\n",pta.x, pta.y, pta.z);
(void) fprintf(stdout,"ptb = (%10.5f %10.5f %10.5f)\n",ptb.x, ptb.y, ptb.z);
(void) fprintf(stdout,"ptc = (%10.5f %10.5f %10.5f)\n",ptc.x, ptc.y, ptc.z);
(void) fprintf(stdout,"%s\n",(intsct) ? "Found Intersection" : "No Intersection");
}
*/
/*
* Find the intersection between a rectangle and a plane
* 4 vertices are specified: v1----v2
* Assume that 4 vertices are sequential, i.e. | |
* v4----v3
*/
int CNpoly4_intsct_plane(a,b,c,d,pta,ptb,ptc,ptd,intpt,npts,verbose)
double a, b, c, d; /* The equation of the plane */
CNpoint *pta, *ptb, *ptc, *ptd; /* Rectangle vertices */
CNpoint intpt[]; /* Intersection coords */
int *npts; /* Number of intersections */
int verbose; /* Verbosity flag for debug */
{
CNpoint pt1, pt2, pt3, pt4, point[4];
double d1, d2, d3, d4;
int in1, in2, in3, in4, nint;
int intsct = CN_FALSE;
int lg01, lg12, lg20;
int i = 0;
/* Initialize */
*npts = 0;
/* Double-check plane equation */
if ((fabs(a)<CN_SMALLER) && (fabs(b)<CN_SMALLER) && (fabs(c)<CN_SMALLER)) {
(void) fprintf(stderr,"The plane is undefined! ");
(void) fprintf(stderr,"Plane equation: %gx + %gy + %gz = %g\n",a,b,c,-d);
return(intsct);
}
/* Normalize the plane equation */
CNnormalize_plane(&a,&b,&c,&d);
/* Check the rectangle first using plane equation : ax + by + cz + d = 0 */
d1 = -1.0 * ( a * pta->x + b * pta->y + c * pta->z);
d2 = -1.0 * ( a * ptb->x + b * ptb->y + c * ptb->z);
d3 = -1.0 * ( a * ptc->x + b * ptc->y + c * ptc->z);
d4 = -1.0 * ( a * ptd->x + b * ptd->y + c * ptd->z);
/*
* if d1, d2, d3, d4 all greater or all less than d0, then no intsct
* If the rectangle is underneath the plane and touches the plane then count
* as no intersection.
* If the rectangle is above the plane and touches the plane then count
* as an intersection.
* This avoids double-intersections if the plane is coincident with an
* edge of the rectangle.
*/
if ( (fabs(d-d1)<CN_SMALLER) && (fabs(d-d2)<CN_SMALLER) &&
(fabs(d-d3)<CN_SMALLER) && (fabs(d-d4)<CN_SMALLER) ){
/* Rectangle is on the plane */
if (verbose) (void) fprintf(stdout,"Plane is parallel to rectangle\n");
intsct = CN_FALSE;
return(intsct);
} else if ( ((d1 >= d ) && (d2 >= d) && (d3 >= d) && (d4 >= d)) ||
((d1 < d ) && (d2 < d) && (d3 < d) && (d4 < d)) ) {
/* Rectangle has points all on one side of plane */
intsct = CN_FALSE;
return(intsct);
}
/* Find intersections of line-segments */
in1 = CNline_intsct_plane(a, b, c, d, pta, ptb, &pt1);
in2 = CNline_intsct_plane(a, b, c, d, ptc, ptb, &pt2);
in3 = CNline_intsct_plane(a, b, c, d, ptc, ptd, &pt3);
in4 = CNline_intsct_plane(a, b, c, d, pta, ptd, &pt4);
if (in1) point[i++]=pt1;
if (in2) point[i++]=pt2;
if (in3) point[i++]=pt3;
if (in4) point[i++]=pt4;
nint = in1 + in2 + in3 + in4;
/* Print intersection info */
if (verbose) {
(void) fprintf(stdout,"%d intersections\n",nint);
for (i=0; i<nint; i++)
(void) fprintf(stdout,"Intersection #%d : (%10.5f %10.5f %10.5f)\n",
i,point[i].x,point[i].y,point[i].z);
}
/* There can be 0 to 4 intersections */
if (nint == 1) {
/*
* One intersection - must be floating point error where
* the plane is at the tip of a vertice
*/
intsct = CN_FALSE;
} else if (nint == 2) {
/*
* Two intersections - just return 2
*/
intpt[0] = point[0];
intpt[1] = point[1];
*npts = 2;
intsct = CN_TRUE;
} else if (nint == 3) {
/*
* Three intersections - check the distance between intersections
* to screen out floating-point-error.
* Possible that 3 points are on the plane...
*/
lg01 = CNlongline(&(point[0]),&(point[1]),1.0e-5);
lg12 = CNlongline(&(point[1]),&(point[2]),1.0e-5);
lg20 = CNlongline(&(point[2]),&(point[0]),1.0e-5);
/* If there are 3 long-lines add all 3 to the list */
if (lg01 && lg12 && lg20) {
if (lg01) {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[1];
}
if (lg12) {
intpt[(*npts)++] = point[1];
intpt[(*npts)++] = point[2];
}
if (lg20) {
intpt[(*npts)++] = point[2];
intpt[(*npts)++] = point[0];
}
} else if (!lg01) {
/* pt0 = pt1, ln12 = ln20 */
if (lg12) {
intpt[(*npts)++] = point[1];
intpt[(*npts)++] = point[2];
}
} else if (!lg12) {
/* pt1 = pt2, ln01 = ln20 */
if (lg01) {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[1];
}
} else if (!lg20) {
/* pt0 = pt2, ln01 = ln21 */
if (lg01) {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[1];
}
}
if ((*npts)>0) intsct = CN_TRUE;
} else if (nint == 4) {
/*
* Four intersections - match up pairs based on whether the
* vertice in between 2 intersections is high or low.
*
* There is a possibility that some points are the same due to
* floating-point error - handle these cases too
*/
/*
if (d1 > d) {
*/
if (d1 < d) {
/* Pairs are (p1,p2) (p3,p4) */
if (CNlongline(&pt1,&pt2,1.0e-5) && CNlongline(&pt3,&pt4,1.0e-5)) {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[1];
intpt[(*npts)++] = point[2];
intpt[(*npts)++] = point[3];
} else {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[2];
}
} else {
/* Pairs are (p1,p4) (p2,p3) */
if (CNlongline(&pt1,&pt4,1.0e-5) && CNlongline(&pt2,&pt3,1.0e-5)) {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[3];
intpt[(*npts)++] = point[1];
intpt[(*npts)++] = point[2];
} else {
intpt[(*npts)++] = point[0];
intpt[(*npts)++] = point[1];
}
}
intsct = CN_TRUE;
} else {
/*
* Zero or non-valid no of intersections
*/
intsct = CN_FALSE;
}
/* Return status */
return(intsct);
}
/*
* Find the intersection between a triangle and a plane
*/
int CNpoly3_intsct_plane(a,b,c,d,pta,ptb,ptc,ptmin,ptmax,verbose)
double a, b, c, d; /* The equation of the plane */
CNpoint *pta, *ptb, *ptc; /* Triangle vertices */
CNpoint *ptmin, *ptmax; /* Intersections */
int verbose; /* Verbosity flag for debug */
{
CNpoint pt1, pt2, pt3, point[3];
double d1, d2, d3;
int in1, in2, in3, nint;
int intsct = CN_FALSE;
int i = 0;
/* Double-check plane equation */
if ((fabs(a)<CN_SMALLER) && (fabs(b)<CN_SMALLER) && (fabs(c)<CN_SMALLER)) {
(void) fprintf(stderr,"The plane is undefined! ");
(void) fprintf(stderr,"Plane equation: %gx + %gy + %gz = %g\n",a,b,c,-d);
return(intsct);
}
/* Normalize the plane equation */
CNnormalize_plane(&a,&b,&c,&d);
/* Check the triangle first using plane equation : ax + by + cz + d = 0 */
d1 = -1.0 * ( a * pta->x + b * pta->y + c * pta->z);
d2 = -1.0 * ( a * ptb->x + b * ptb->y + c * ptb->z);
d3 = -1.0 * ( a * ptc->x + b * ptc->y + c * ptc->z);
/*
* if d1, d2, d3 all greater or all less than d0, then no intsct
* If the triangle is underneath the plane and touches the plane then count
* as no intersection.
* If the triangle is above the plane and touches the plane then count
* as an intersection.
* This avoids double-intersections if the plane is coincident with an
* edge of the triangle.
*/
if ( (fabs(d-d1)<CN_SMALLER) &&
(fabs(d-d2)<CN_SMALLER) &&
(fabs(d-d3)<CN_SMALLER) ){
/* Tria is on the plane */
if (verbose) (void) fprintf(stdout,"Plane is parallel to triangle\n");
intsct = CN_FALSE;
return(intsct);
} else if ( ((d1 >= d ) && (d2 >= d) && (d3 >= d)) ||
((d1 < d ) && (d2 < d) && (d3 < d)) ) {
/* Tria has points all on one side of plane */
intsct = CN_FALSE;
return(intsct);
}
/* Find intersections of line-segments */
in1 = CNline_intsct_plane(a, b, c, d, pta, ptb, &pt1);
in2 = CNline_intsct_plane(a, b, c, d, ptc, ptb, &pt2);
in3 = CNline_intsct_plane(a, b, c, d, ptc, pta, &pt3);
if (in1) point[i++]=pt1;
if (in2) point[i++]=pt2;
if (in3) point[i++]=pt3;
nint = in1 + in2 + in3;
if (verbose) (void) fprintf(stdout,"%d intersections\n",nint);
/* There can be 0 to 3 intersections */
if (nint == 1) {
/*
* One intersection - must be floating point error where
* the plane is at the tip of the triangle
*/
intsct = CN_FALSE;
} else if (nint == 2) {
/*
* Two intersections - just return 2
*/
*ptmin = point[0];
*ptmax = point[1];
intsct = CN_TRUE;
} else if (nint == 3) {
/*
* Three intersections - two of these must be pretty close
*/
if (verbose) {
for (i=0; i<nint; i++)
(void) fprintf(stdout,"Intersection #%d : (%10.5f %10.5f %10.5f)\n",
i,point[i].x,point[i].y,point[i].z);
}
/* Get the line-segment */
if ( (fabs(point[0].x - point[1].x) < CN_SMALLER) &&
(fabs(point[0].y - point[1].y) < CN_SMALLER) &&
(fabs(point[0].z - point[1].z) < CN_SMALLER) ) {
*ptmin = point[0];
*ptmax = point[2];
} else {
*ptmin = point[0];
*ptmax = point[1];
}
intsct = CN_TRUE;
} else {
/*
* Zero or non-valid no of intersections
*/
intsct = CN_FALSE;
}
/* Return status */
return(intsct);
}
/*
* find the intersection values between a line-segment and a plane
*/
int CNline_intsct_plane(a, b, c, d, pta, ptb, ptc)
double a, b, c, d; /* The equation of the plane */
CNpoint *pta, *ptb; /* The two points on the line-segment */
CNpoint *ptc; /* The intersection */
{
int intsct = CN_FALSE;
double d1, d2, t;
/* Double-check plane equation */
if ((fabs(a)<CN_SMALLER) && (fabs(b)<CN_SMALLER) && (fabs(c)<CN_SMALLER)) {
(void) fprintf(stderr,"The plane is undefined! ");
(void) fprintf(stderr,"Plane equation: %gx + %gy + %gz = %g\n",a,b,c,-d);
return(intsct);
}
/* Get plane equations for 2 points */
d1 = -1.0 * ( a * pta->x + b * pta->y + c * pta->z);
d2 = -1.0 * ( a * ptb->x + b * ptb->y + c * ptb->z);
/*
* We need to avoid multiple points where a joint of 2 lines
* falls exactly on a plane. In such a case, screen the lines first
* so that one line is "above" and one line intersects the plane.
* But can't do this here because then the order of the points on the
* line makes a difference.
*/
if (fabs(d2-d1) < CN_SMALLER) {
/* The line lies on or is parallel to the plane */
intsct = CN_FALSE;
return(intsct);
} else if ( ((d1 > d) && (d2 > d)) || ((d1 < d) && (d2 < d)) ) {
/* Line has points all on one side of the planes */
intsct = CN_FALSE;
return(intsct);
}
/*
* Let the parameter t overlap a bit.
* This means that if one point of the line is exactly on the plane,
* it will be counted as an intersection regardless of its position
* on the line.
*/
/* Find the intersection */
t = (d - d1) / (d2 - d1);
if ((t > -CN_SMALLER) && (t <= 1.0+CN_SMALLER)) {
intsct = CN_TRUE;
if (t < 0.5) {
ptc->x = pta->x + t*(ptb->x - pta->x);
ptc->y = pta->y + t*(ptb->y - pta->y);
ptc->z = pta->z + t*(ptb->z - pta->z);
} else {
/*
* This is to prevent problems when t is very small,
* e.g. t=1e-20, so that 1-t=1. In such cases, the order
* of points makes a difference. This if-else statement
* circumvents the problem by switching the order of points.
*/
t = (d - d2) / (d1 - d2);
ptc->x = ptb->x + t*(pta->x - ptb->x);
ptc->y = ptb->y + t*(pta->y - ptb->y);
ptc->z = ptb->z + t*(pta->z - ptb->z);
}
}
/* Return status */
return(intsct);
}
/*
* find out if a line-segment is long or short
*
* This comparison needs to be done on a relative basis
*/
int CNlongline(pta,ptb,delta)
CNpoint *pta,*ptb;
double delta;
{
int longln = CN_TRUE;
double dx,dy,dz,dlsq;
dx = pta->x - ptb->x;
dy = pta->y - ptb->y;
dz = pta->z - ptb->z;
dlsq = dx*dx + dy*dy + dz*dz;
/*
* Delta is the boundary which is larger than dx,dy,dz
* but delta could be zero
*/
delta = 1e-15*delta*delta;
if (delta < CN_SMALLER) delta = CN_SMALLER;
longln = (dlsq > delta) ? CN_TRUE : CN_FALSE;
return(longln);
}
/*
* find out if a line-segment is long or short
*
* This comparison needs to be done on a relative basis
*/
int CNlongline_old(pta,ptb)
CNpoint *pta,*ptb;
{
int longln = CN_TRUE;
double dx,dy,dz;
double xm,ym,zm;
dx = fabs(pta->x - ptb->x); xm = fabs(pta->x + ptb->x);
dy = fabs(pta->y - ptb->y); ym = fabs(pta->y + ptb->y);
dz = fabs(pta->z - ptb->z); zm = fabs(pta->z + ptb->z);
if (xm < CN_SMALLER)
longln = (dx > CN_SMALL) ? CN_TRUE : CN_FALSE;
else
longln = (dx/xm > CN_SMALL) ? CN_TRUE : CN_FALSE;
if (longln) return(longln);
if (ym < CN_SMALLER)
longln = (dy > CN_SMALL) ? CN_TRUE : CN_FALSE;
else
longln = (dy/ym > CN_SMALL) ? CN_TRUE : CN_FALSE;
if (longln) return(longln);
if (zm < CN_SMALLER)
longln = (dz > CN_SMALL) ? CN_TRUE : CN_FALSE;
else
longln = (dz/zm > CN_SMALL) ? CN_TRUE : CN_FALSE;
if (longln) return(longln);
return(longln);
}
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