1 /*****************************************************************************
5 ** Purpose: Routines for phantom objects
6 ** Progammer: Kevin Rosenberg
7 ** Date Started: Aug 1984
9 ** This is part of the CTSim program
10 ** Copyright (C) 1983-2000 Kevin Rosenberg
12 ** $Id: phantom.cpp,v 1.4 2000/06/22 10:17:28 kevin Exp $
14 ** This program is free software; you can redistribute it and/or modify
15 ** it under the terms of the GNU General Public License (version 2) as
16 ** published by the Free Software Foundation.
18 ** This program is distributed in the hope that it will be useful,
19 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
20 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 ** GNU General Public License for more details.
23 ** You should have received a copy of the GNU General Public License
24 ** along with this program; if not, write to the Free Software
25 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 ******************************************************************************/
31 // CLASS IDENTIFICATION
35 Phantom::Phantom (void)
41 Phantom::Phantom (const char* const phmName)
44 createFromPhantom (phmName);
56 m_composition = P_PELEMS;
61 Phantom::~Phantom (void)
63 for (PElemIterator i = m_listPElem.begin(); i != m_listPElem.end(); i++) {
70 Phantom::convertPhantomIDToName (const PhantomID phmID)
72 const char *name = "";
74 if (phmID == PHM_HERMAN)
75 name = PHM_HERMAN_STR;
76 else if (phmID == PHM_BHERMAN)
77 name = PHM_BHERMAN_STR;
78 else if (phmID == PHM_ROWLAND)
79 name = PHM_ROWLAND_STR;
80 else if (phmID == PHM_BROWLAND)
81 name = PHM_BROWLAND_STR;
82 else if (phmID == PHM_UNITPULSE)
83 name = PHM_UNITPULSE_STR;
89 Phantom::convertNameToPhantomID (const char* const phmName)
93 if (strcasecmp (phmName, PHM_HERMAN_STR) == 0)
95 else if (strcasecmp (phmName, PHM_BHERMAN_STR) == 0)
97 else if (strcasecmp (phmName, PHM_ROWLAND_STR) == 0)
99 else if (strcasecmp (phmName, PHM_BROWLAND_STR) == 0)
101 else if (strcasecmp (phmName, PHM_UNITPULSE_STR) == 0)
111 Phantom::createFromPhantom (const char* const phmName)
113 PhantomID phmid = convertNameToPhantomID (phmName);
116 createFromPhantom (phmid);
120 Phantom::createFromPhantom (const PhantomID phmid)
128 addStdHermanBordered();
134 addStdRowlandBordered ();
137 m_composition = P_UNIT_PULSE;
138 addPElem ("rectangle", 0., 0., 100., 100., 0., 0.); // outline
139 addPElem ("ellipse", 0., 0., 1., 1., 0., 1.); // pulse
142 sys_error (ERR_WARNING, "Illegal phantom id %d\n", phmid);
143 m_name += " -- INVALID";
155 /* METHOD IDENTIFICATION
156 * createFromFile Add PhantomElements from file
159 * createFromFile (filename)
162 * true if pelem were added
163 * false if an pelem not added
167 Phantom::createFromFile (const char* const fname)
169 bool stoploop = false;
173 if ((fp = fopen (fname, "r")) == NULL)
177 double cx, cy, u, v, rot, dens;
179 int n = fscanf (fp, "%79s %lf %lf %lf %lf %lf %lf",
180 pelemtype, &cx, &cy, &u, &v, &rot, &dens);
182 if (n == EOF || n == 0) { /* end of file */
189 addPElem (pelemtype, cx, cy, u, v, rot, dens);
192 } while (stoploop == false);
204 * addPElem (type, cx, cy, u, v, rot, atten)
205 * char *type type of pelem (box, ellipse, etc)
206 * double cx, cy pelem center
207 * double u,v pelem size
208 * double rot rotation angle of pelem (in degrees)
209 * double atten x-ray attenuation cooefficient
213 Phantom::addPElem (const char *type, const double cx, const double cy, const double u, const double v, const double rot, const double atten)
215 PhantomElement *pelem = new PhantomElement (type, cx, cy, u, v, rot, atten);
217 m_listPElem.push_front (pelem);
219 // update phantom limits
220 if (m_xmin > pelem->xmin()) m_xmin = pelem->xmin();
221 if (m_xmax < pelem->xmax()) m_xmax = pelem->xmax();
222 if (m_ymin > pelem->ymin()) m_ymin = pelem->ymin();
223 if (m_ymax < pelem->ymax()) m_ymax = pelem->ymax();
225 if (m_diameter < pelem->diameter())
226 m_diameter = pelem->diameter();
228 // m_diameter = lineLength(m_xmin, m_ymin, m_xmax, m_ymax);
234 /*----------------------------------------------------------------------*/
235 /* Input-Output Routines */
236 /*----------------------------------------------------------------------*/
240 * print Print vertices of Phantom pelems
247 Phantom::print (void) const
249 printf("PRINTING Phantom\n\n");
250 printf("number of pelems in Phantom = %d\n", m_nPElem);
251 printf("limits: xmin=%8.2g ymin=%8.2g xmax=%8.2g ymax=%8.2g\n",
252 m_xmin, m_ymin, m_xmax, m_ymax);
254 for (PElemIterator i = m_listPElem.begin(); i != m_listPElem.end(); i++) {
256 printf("# pts=%3d atten = %7.4f rot = %7.2f (deg)\n",
257 (*i)->nOutlinePoints(), (*i)->atten(), convertRadiansToDegrees ((*i)->rot()));
259 printf("xmin=%7.3g ymin=%7.3g xmax=%7.3g ymax=%7.3g\n",
260 (*i)->xmin(), (*i)->ymin(), (*i)->xmax(), (*i)->ymax());
262 // for (int i = 0; i < m_nPoints; i++)
263 // printf("\t%8.3g %8.3g\n", i->xOutline()[i], i->yOutline()[i]);
269 * show Show vector outline of Phantom to user
277 Phantom::show (void) const
279 double wsize = m_xmax - m_xmin;
280 double xmin = m_xmin;
281 double ymin = m_ymin;
285 if ((m_ymax - m_ymin) > wsize)
286 wsize = m_ymax - m_ymin;
292 printf("Drawing Phantom:\n\n");
293 printf(" data limits: %9.3g, %9.3g, %9.3g, %9.3g\n",
294 m_xmin, m_ymin, m_xmax, m_ymax);
295 printf(" window size: %9.3g, %9.3g, %9.3g, %9.3g\n",
296 xmin, ymin, xmax, ymax);
298 gid = sgp2_init(0, 0, "Phantom Show");
299 sgp2_window (xmin, ymin, xmax, ymax);
309 * draw Draw vector outline of Phantom
317 Phantom::draw (void) const
319 for (PElemIterator i = m_listPElem.begin(); i != m_listPElem.end(); i++)
320 sgp2_polyline_abs ((*i)->xOutline(), (*i)->yOutline(), (*i)->nOutlinePoints());
326 * addStdRowland Make head phantom of S.W. Rowland
329 * S. W. Rowland, "Computer Implementation of Image Reconstruction
330 * Formulas", in "Image Reconstruction from Projections: Implementation
331 * and Applications", edited by G. T. Herman, 1978.
335 Phantom::addStdRowland (void)
337 addPElem("ellipse", 0.0000, 0.0000, 0.6900, 0.9200, 0.0, 1.00);
338 addPElem("ellipse", 0.0000, -0.0184, 0.6624, 0.8740, 0.0, -0.98);
339 addPElem("ellipse", 0.2200, 0.0000, 0.1100, 0.3100, -18.0, -0.02);
340 addPElem("ellipse", -0.2200, 0.0000, 0.1600, 0.4100, 18.0, -0.02);
341 addPElem("ellipse", 0.0000, 0.3500, 0.2100, 0.2500, 0.0, 0.01);
342 addPElem("ellipse", 0.0000, 0.1000, 0.0460, 0.0460, 0.0, 0.01);
343 addPElem("ellipse", 0.0000, -0.1000, 0.0460, 0.0460, 0.0, 0.01);
344 addPElem("ellipse", -0.0800, -0.6050, 0.0460, 0.0230, 0.0, 0.01);
345 addPElem("ellipse", 0.0000, -0.6050, 0.0230, 0.0230, 0.0, 0.01);
346 addPElem("ellipse", 0.0600, -0.6050, 0.0230, 0.0230, 0.0, 0.01);
347 addPElem("ellipse", 0.5538, -0.3858, 0.0330, 0.2060, -18.0, 0.03);
351 Phantom::addStdRowlandBordered (void)
354 addPElem ("ellipse", 0.000, 0.0000, 0.7500, 1.000, 0.0, 0.00);
358 * addStdHerman Standard head phantom of G. T. Herman
361 * G. T. Herman, "Image Reconstructions from Projections: The Fundementals
362 * of Computed Tomography", 1979.
366 Phantom::addStdHerman (void)
368 addPElem("ellipse", 0.000, 1.50, 0.375, 0.3000, 90.00, -0.003);
369 addPElem("ellipse", 0.675, -0.75, 0.225, 0.1500, 140.00, 0.010);
370 addPElem("ellipse", 0.750, 1.50, 0.375, 0.2250, 50.00, 0.003);
371 addPElem("segment", 1.375, -7.50, 1.100, 0.6250, 19.20, -0.204);
372 addPElem("segment", 1.375, -7.50, 1.100, 4.3200, 19.21, 0.204);
373 addPElem("segment", 0.000, -2.25, 1.125, 0.3750, 0.00, -0.003);
374 addPElem("segment", 0.000, -2.25, 1.125, 3.0000, 0.00, 0.003);
375 addPElem("segment", -1.000, 3.75, 1.000, 0.5000, 135.00, -0.003);
376 addPElem("segment", -1.000, 3.75, 1.000, 3.0000, 135.00, 0.003);
377 addPElem("segment", 1.000, 3.75, 1.000, 0.5000, 225.00, -0.003);
378 addPElem("segment", 1.000, 3.75, 1.000, 3.0000, 225.00, 0.003);
379 addPElem("triangle", 5.025, 3.75, 1.125, 0.5000, 110.75, 0.206);
380 addPElem("triangle",-5.025, 3.75, 1.125, 0.9000,-110.75, 0.206);
381 addPElem("ellipse", 0.000, 0.00, 8.625, 6.4687, 90.00, 0.416);
382 addPElem("ellipse", 0.000, 0.00, 7.875, 5.7187, 90.00, -0.206);
386 Phantom::addStdHermanBordered (void)
388 addPElem("ellipse", 0., 0., 6.6, 5.9, 90., 0.);
393 * convertToImagefile Make image array from Phantom
396 * pic_to_imagefile (pic, im, nsample)
397 * Phantom& pic Phantom definitions
398 * ImageFile *im Computed pixel array
399 * int nsample Number of samples along each axis for each pixel
400 * (total samples per pixel = nsample * nsample)
404 Phantom::convertToImagefile (ImageFile& im, const int in_nsample, const int trace) const
406 convertToImagefile (im, in_nsample, trace, 0, im.nx());
410 Phantom::convertToImagefile (ImageFile& im, const int in_nsample, const int trace, const int colStart, const int colCount) const
414 if (nx < 2 || ny < 2)
417 int nsample = in_nsample;
421 double dx = m_xmax - m_xmin;
422 double dy = m_ymax - m_ymin;
423 double xcent = m_xmin + dx / 2;
424 double ycent = m_ymin + dy / 2;
425 double phmlen = (dx > dy ? dx : dy);
427 double phmradius = phmlen / 2;
429 double xmin = xcent - phmradius;
430 double xmax = xcent + phmradius;
431 double ymin = ycent - phmradius;
432 double ymax = ycent + phmradius;
434 // Each pixel holds the average of the intensity of the cell with (ix,iy) at the center of the pixel
435 // Set major increments so that the last cell v[nx-1][ny-1] will start at xmax - xinc, ymax - yinc).
436 // Set minor increments so that sample points are centered in cell
438 double xinc = (xmax - xmin) / nx;
439 double yinc = (ymax - ymin) / ny;
441 double kxinc = xinc / nsample; /* interval between samples */
442 double kyinc = yinc / nsample;
443 double kxofs = kxinc / 2; /* offset of 1st point */
444 double kyofs = kyinc / 2;
446 im.setAxisExtent (xmin, xmax, ymin, ymax);
447 im.setAxisIncrement (xinc, yinc);
449 ImageFileArray v = im.getArray();
451 double x_start = xmin + (colStart * xinc);
452 for (PElemConstIterator pelem = m_listPElem.begin(); pelem != m_listPElem.end(); pelem++) {
455 for (ix = 0, x = x_start; ix < colCount; ix++, x += xinc) {
456 for (iy = 0, y = ymin; iy < ny; iy++, y += yinc) {
457 for (kx = 0, xi = x + kxofs; kx < nsample; kx++, xi += kxinc) {
458 for (ky = 0, yi = y + kyofs; ky < nsample; ky++, yi += kyinc)
459 if ((*pelem)->isPointInside (xi, yi, PHM_COORD) == TRUE)
460 v[ix][iy] += (*pelem)->atten();
468 double factor = 1.0 / (nsample * nsample);
470 for (int ix = 0; ix < colCount; ix++)
471 for (int iy = 0; iy < ny; iy++)
476 ////////////////////////////////////////////////////////////////////////////////////////////////////////
477 // CLASS IDENTIFICATION
483 ////////////////////////////////////////////////////////////////////////////////////////////////////////
486 PhantomElement::PhantomElement (const char *type, const double cx, const double cy, const double u, const double v, const double rot, const double atten)
487 : m_cx(cx), m_cy(cy), m_u(u), m_v(v), m_atten(atten), m_nPoints(0), m_xOutline(0), m_yOutline(0)
489 m_rot = convertDegreesToRadians (rot); // convert angle to radians
491 m_type = convertNameToType (type);
493 makeTransformMatrices (); // calc transform matrices between phantom and normalized phantomelement
494 makeVectorOutline (); // calculate vector outline of pelem
496 // Find maximum diameter of Object
498 for (int i = 0; i < m_nPoints; i++) {
499 double r2 = (m_xOutline[i] * m_xOutline[i]) + (m_yOutline[i] * m_yOutline[i]);
503 m_diameter = 2 * sqrt( r2Max );
505 m_rectLimits[0] = m_xmin; m_rectLimits[1] = m_ymin;
506 m_rectLimits[2] = m_xmax; m_rectLimits[3] = m_ymax;
510 PhantomElement::~PhantomElement (void)
517 PhantomElement::convertNameToType (const char* const typeName)
519 PhmElemType type = PELEM_INVALID;
521 if (strcasecmp (typeName, "rectangle") == 0)
522 type = PELEM_RECTANGLE;
523 else if (strcasecmp (typeName, "triangle") == 0)
524 type = PELEM_TRIANGLE;
525 else if (strcasecmp (typeName, "ellipse") == 0)
526 type = PELEM_ELLIPSE;
527 else if (strcasecmp (typeName, "sector") == 0)
529 else if (strcasecmp (typeName, "segment") == 0)
530 type = PELEM_SEGMENT;
532 sys_error (ERR_WARNING, "Unknown PhantomElement type %s [PhantomElement::PhantomElement]", type);
538 PhantomElement::makeTransformMatrices (void)
542 // To map normalized Pelem coords to world Phantom
545 // translate by (cx, cy)
547 scale_mtx2 (m_xformObjToPhm, m_u, m_v);
548 rot_mtx2 (temp, m_rot);
549 mult_mtx2 (m_xformObjToPhm, temp, m_xformObjToPhm);
550 xlat_mtx2 (temp, m_cx, m_cy);
551 mult_mtx2 (m_xformObjToPhm, temp, m_xformObjToPhm);
553 // to map world Phantom coodinates to normalized PElem coords
554 // translate by (-cx, -cy)
556 // scale by (1/u, 1/v)
558 xlat_mtx2 (m_xformPhmToObj, -m_cx, -m_cy);
559 rot_mtx2 (temp, -m_rot);
560 mult_mtx2 (m_xformPhmToObj, temp, m_xformPhmToObj);
561 scale_mtx2 (temp, 1 / m_u, 1 / m_v);
562 mult_mtx2 (m_xformPhmToObj, temp, m_xformPhmToObj);
567 * pelem_make_points INTERNAL routine to calculate point array for an pelem
570 * makepelempts (pelem)
571 * PELEM *pelem pelem whose points we are calculating
574 * Called by phm_add_pelem()
578 PhantomElement::makeVectorOutline (void)
580 double radius, theta, start, stop;
586 case PELEM_RECTANGLE:
588 m_xOutline = new double [m_nPoints];
589 m_yOutline = new double [m_nPoints];
590 m_xOutline[0] =-m_u; m_yOutline[0] =-m_v;
591 m_xOutline[1] = m_u; m_yOutline[1] =-m_v;
592 m_xOutline[2] = m_u; m_yOutline[2] = m_v;
593 m_xOutline[3] =-m_u; m_yOutline[3] = m_v;
594 m_xOutline[4] =-m_u; m_yOutline[4] =-m_v;
598 m_xOutline = new double [m_nPoints];
599 m_yOutline = new double [m_nPoints];
600 m_xOutline[0] =-m_u; m_yOutline[0] = 0.0;
601 m_xOutline[1] = m_u; m_yOutline[1] = 0.0;
602 m_xOutline[2] = 0.0; m_yOutline[2] = m_v;
603 m_xOutline[3] =-m_u; m_yOutline[3] = 0.0;
606 cpts = numCirclePoints (TWOPI);
608 m_xOutline = new double [m_nPoints];
609 m_yOutline = new double [m_nPoints];
610 calcEllipsePoints (m_xOutline, m_yOutline, cpts, m_u, m_v);
613 radius = sqrt(m_u * m_u + m_v * m_v);
614 theta = atan(m_u / m_v); // angle with y-axis
615 start = 3.0 * HALFPI - theta;
616 stop = 3.0 * HALFPI + theta;
617 cpts = numCirclePoints (stop - start);
618 m_nPoints = 3 + cpts;
619 m_xOutline = new double [m_nPoints];
620 m_yOutline = new double [m_nPoints];
622 m_xOutline[0] = 0.0; m_yOutline[0] = m_v;
623 m_xOutline[1] =-m_u; m_yOutline[1] = 0.0;
624 calcArcPoints (&m_xOutline[2], &m_yOutline[2], cpts, 0.0, m_v, radius, start, stop);
625 m_xOutline[cpts + 2] = 0.0;
626 m_yOutline[cpts + 2] = m_v;
629 radius = sqrt(m_u * m_u + m_v * m_v);
630 theta = atan (m_u / m_v); // angle with y-axis
631 start = 3.0 * HALFPI - theta;
632 stop = 3.0 * HALFPI + theta;
634 cpts = numCirclePoints (stop - start);
635 m_nPoints = cpts + 1;
636 m_xOutline = new double [m_nPoints];
637 m_yOutline = new double [m_nPoints];
639 calcArcPoints (m_xOutline, m_yOutline, cpts, 0.0, m_v, radius, start, stop);
640 m_xOutline[cpts] = -m_u;
641 m_yOutline[cpts] = 0.0;
644 sys_error(ERR_WARNING, "illegal pelem type %d [makeVectorOutline]", m_type);
648 rotate2d (m_xOutline, m_yOutline, m_nPoints, m_rot);
649 xlat2d (m_xOutline, m_yOutline, m_nPoints, m_cx, m_cy);
651 minmax_array (m_xOutline, m_nPoints, m_xmin, m_xmax);
652 minmax_array (m_yOutline, m_nPoints, m_ymin, m_ymax);
654 // increase pelem extent by SCALE_PELEM_EXTENT to eliminate chance of
655 // missing actual pelem maximum due to polygonal sampling
657 xfact = (m_xmax - m_xmin) * SCALE_PELEM_EXTENT;
658 yfact = (m_ymax - m_ymin) * SCALE_PELEM_EXTENT;
668 * calc_arc Calculate outline of a arc of a circle
671 * calc_arc (x, y, xcent, ycent, pts, r, start, stop)
672 * double x[], y[]; Array of points
673 * int pts Number of points in array
674 * double xcent, ycent Center of cirlce
675 * double r Radius of circle
676 * double start, stop Beginning & ending angles
680 PhantomElement::calcArcPoints (double x[], double y[], const int pts, const double xcent, const double ycent, const double r, const double start, const double stop)
683 sys_error (ERR_WARNING, "negative or zero radius in calc_arc()");
685 double theta = (stop - start) / (pts - 1); // angle incr. between points
686 double c = cos(theta);
687 double s = sin(theta);
689 x[0] = r * cos (start) + xcent;
690 y[0] = r * sin (start) + ycent;
692 double xp = x[0] - xcent;
693 double yp = y[0] - ycent;
694 for (int i = 1; i < pts; i++) {
695 double xc = c * xp - s * yp;
696 double yc = s * xp + c * yp;
705 // PhantomElement::calcEllipsePoints Calculate outline of a ellipse
708 // calcEllipsePoints ()
713 PhantomElement::calcEllipsePoints (double x[], double y[], const int pts, const double u, const double v)
715 calcArcPoints (x, y, m_nPoints, 0.0, 0.0, 1.0, 0.0, TWOPI); // make a unit circle
716 scale2d (x, y, m_nPoints, m_u, m_v); // scale to ellipse
721 * circle_pts Calculate number of points to use for circle segment
724 * n = circle_pts (theta)
725 * int n Number of points to use for arc
726 * double theta Length of arc in radians
730 PhantomElement::numCirclePoints (double theta)
732 theta = clamp (theta, 0., TWOPI);
734 return static_cast<int> (POINTS_PER_CIRCLE * theta / TWOPI + 1.5);
739 PhantomElement::clipLineWorldCoords (double& x1, double& y1, double& x2, double &y2) const
741 /* check if ray is outside of pelem extents */
742 double cx1 = x1, cy1 = y1, cx2 = x2, cy2 = y2;
743 if (! clip_rect (cx1, cy1, cx2, cy2, m_rectLimits))
746 // convert phantom coordinates to pelem coordinates
747 xform_mtx2 (m_xformPhmToObj, x1, y1);
748 xform_mtx2 (m_xformPhmToObj, x2, y2);
750 if (! clipLineNormalizedCoords (x1, y1, x2, y2))
753 // convert standard pelem coordinates back to phantom coordinates
754 xform_mtx2 (m_xformObjToPhm, x1, y1);
755 xform_mtx2 (m_xformObjToPhm, x2, y2);
762 * pelem_clip_line Clip pelem against an arbitrary line
765 * pelem_clip_line (pelem, x1, y1, x2, y2)
766 * PhantomElement& pelem; Pelem to be clipped
767 * double *x1, *y1, *x2, *y2 Endpoints of line to be clipped
770 * true if line passes through pelem
771 * (x1, y1, x2, y2 hold coordinates of new line)
772 * false if line do not pass through pelem
773 * (x1, y1, x2, y2 are undefined)
777 PhantomElement::clipLineNormalizedCoords (double& x1, double& y1, double& x2, double& y2) const
782 case PELEM_RECTANGLE:
784 rect[0] = -1.0; rect[1] = -1.0;
785 rect[2] = 1.0; rect[3] = 1.0;
786 accept = clip_rect (x1, y1, x2, y2, rect);
789 accept = clip_circle (x1, y1, x2, y2, 0.0, 0.0, 1.0, 0.0, 0.0);
792 accept = clip_triangle (x1, y1, x2, y2, 1.0, 1.0, true);
795 accept = clip_segment (x1, y1, x2, y2, m_u, m_v);
798 accept = clip_sector (x1, y1, x2, y2, m_u, m_v);
801 sys_error (ERR_WARNING, "Illegal pelem type %d [pelem_clip_line]", m_type);
809 // METHOD IDENTIFICATION
810 // PhantomElement::isPointInside Check if point is inside pelem
813 // is_point_inside (pelem, x, y, coord_type)
814 // double x, y Point to see if lies in pelem
815 // int coord_type Coordinate type (PELEM_COORD or PHM_COORD)
818 // true if point lies within pelem
819 // false if point lies outside of pelem
822 PhantomElement::isPointInside (double x, double y, const CoordType coord_type)
824 if (coord_type == PHM_COORD) {
825 xform_mtx2 (m_xformPhmToObj, x, y);
826 } else if (coord_type != PELEM_COORD) {
827 sys_error(ERR_WARNING, "Illegal coordinate type in pelem_is_point_inside");
832 case PELEM_RECTANGLE:
833 if (x > 1. || x < -1. || y > 1. || y < -1.)
839 if (y < 0. || y > 1. - x || y > 1. + x)
845 if (x > 1. || x < -1. || y > 1. || y < -1.)
847 if (x * x + y * y > 1.) // check if inside unit circle
853 // for clipping segments & sectors, must NOT scale by (1/u, 1/v)
854 // because this destroys information about size of arc component
857 if (x > 1. || x < -1. || y > 0.)
858 return (false); // clip against y > 0
859 x *= m_u; // put back u & v scale
861 if (x * x + (y-m_v) * (y-m_v) > m_u * m_u + m_v * m_v)
862 return (false); // clip against circle, r = sqrt(@)
867 if (x > 1. || x < -1. || y > 1.) // extent
869 if (y > 1. - x || y > 1. + x) // triangle
870 return (false); // clip against triangle
871 x *= m_u; // circle: put back u & v scale
873 if (x * x + (y-m_v) * (y-m_v) > m_u * m_u + m_v * m_v)
874 return (false); // clip against circle
879 sys_error (ERR_WARNING, "Illegal pelem type in pelem_is_point_inside()");