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/** R : A Computer Language for Statistical Data Analysis* Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka* Copyright (C) 1997-2000 Robert Gentleman, Ross Ihaka and the R core team.** This program is free software; you can redistribute it and/or modify* it under the terms of the GNU General Public License as published by* the Free Software Foundation; either version 2 of the License, or* (at your option) any later version.** This program is distributed in the hope that it will be useful,* but WITHOUT ANY WARRANTY; without even the implied warranty of* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the* GNU General Public License for more details.** You should have received a copy of the GNU General Public License* along with this program; if not, write to the Free Software* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA*/#ifdef HAVE_CONFIG_H#include <config.h>#endif#include "Defn.h"#include "Mathlib.h"#include "Graphics.h"#include "Print.h"#ifndef HAVE_HYPOT# define hypot pythag#endif/* Conversion of degrees to radians */#define DegToRad(x) (0.01745329251994329576 * x)/* Definitions of data structures for vectors and *//* transformations in homogeneous 3d coordinates */typedef double Vector3d[4];typedef double Trans3d[4][4];/* The viewing transformation matrix. */static SEXP gcall;static Trans3d VT;static void TransVector (Vector3d u, Trans3d T, Vector3d v){double sum;int i, j;for (i = 0; i < 4; i++) {sum = 0;for (j = 0; j < 4; j++)sum = sum + u[j] * T[j][i];v[i] = sum;}}static void Accumulate (Trans3d T){Trans3d U;double sum;int i, j, k;for (i = 0; i < 4; i++) {for (j = 0; j < 4; j++) {sum = 0;for (k = 0; k < 4; k++)sum = sum + VT[i][k] * T[k][j];U[i][j] = sum;}}for (i = 0; i < 4; i++)for (j = 0; j < 4; j++)VT[i][j] = U[i][j];}static void SetToIdentity (Trans3d T){int i, j;for (i = 0; i < 4; i++) {for (j = 0; j < 4; j++)T[i][j] = 0;T[i][i] = 1;}}static void Translate (double x, double y, double z){Trans3d T;SetToIdentity(T);T[3][0] = x;T[3][1] = y;T[3][2] = z;Accumulate(T);}static void Scale (double x, double y, double z){Trans3d T;SetToIdentity(T);T[0][0] = x;T[1][1] = y;T[2][2] = z;Accumulate(T);}static void XRotate (double angle){double c, s;Trans3d T;SetToIdentity(T);c = cos(DegToRad(angle));s = sin(DegToRad(angle));T[1][1] = c;T[2][1] = -s;T[2][2] = c;T[1][2] = s;Accumulate(T);}static void YRotate (double angle){double c, s;Trans3d T;SetToIdentity(T);c = cos(DegToRad(angle));s = sin(DegToRad(angle));T[0][0] = c;T[2][0] = s;T[2][2] = c;T[0][2] = -s;Accumulate(T);}static void ZRotate (double angle){double c, s;Trans3d T;SetToIdentity(T);c = cos(DegToRad(angle));s = sin(DegToRad(angle));T[0][0] = c;T[1][0] = -s;T[1][1] = c;T[0][1] = s;Accumulate(T);}static void Perspective (double d){Trans3d T;SetToIdentity(T);T[2][3] = -1 / d;Accumulate(T);}/* Stuff for labels on contour plotsOriginally written by Nicholas HildrethAdapted by Paul Murrell*/staticvoid FindCorners(double width, double height, SEXP label,double x0, double y0, double x1, double y1,DevDesc *dd) {double delta = height / width;double dx = GConvertXUnits(x1 - x0, USER, INCHES, dd) * delta;double dy = GConvertYUnits(y1 - y0, USER, INCHES, dd) * delta;dx = GConvertYUnits(dx, INCHES, USER, dd);dy = GConvertXUnits(dy, INCHES, USER, dd);REAL(label)[0] = x0 + dy;REAL(label)[4] = y0 - dx;REAL(label)[1] = x0 - dy;REAL(label)[5] = y0 + dx;REAL(label)[3] = x1 + dy;REAL(label)[7] = y1 - dx;REAL(label)[2] = x1 - dy;REAL(label)[6] = y1 + dx;}staticint TestLabelIntersection(SEXP label1, SEXP label2) {int i, j, l1, l2;double Ax, Bx, Ay, By, ax, ay, bx, by, q1, q2;double dom;double result1, result2;for (i = 0; i < 4; i++) {Ax = REAL(label1)[i];Ay = REAL(label1)[i+4];Bx = REAL(label1)[(i+1)%4];By = REAL(label1)[(i+1)%4+4];for (j = 0; j < 4; j++) {ax = REAL(label2)[j];ay = REAL(label2)[j+4];bx = REAL(label2)[(j+1)%4];by = REAL(label2)[(j+1)%4+4];q1 = Ax*(ay-by);q2 = Ay*(bx-ax);dom = Bx*by - Bx*ay - Ax*by + Ax*ay - bx*By + bx*Ay + ax*By - ax*Ay;if (dom == 0.0) {result1 = -1;result2 = -1;}else {result1 = (bx*Ay - ax*Ay - ay*bx - Ax*by + Ax*ay + by*ax) / dom;if (bx - ax == 0.0) {if (by - ay == 0.0)result2 = -1;elseresult2 = (Ay + (By - Ay) * result1 - ay) / (by - ay);}elseresult2 = (Ax + (Bx - Ax) * result1 - ax) / (bx - ax);}l1 = (result1 >= 0.0) && (result1 <= 1.0);l2 = (result2 >= 0.0) && (result2 <= 1.0);if (l1 && l2) return 1;}}return 0;}/*** Checks whether a label window is inside view region ***/static int LabelInsideWindow(SEXP label, DevDesc *dd) {int i = 0;double x, y;while (i < 4) {x = REAL(label)[i];y = REAL(label)[i+4];GConvert(&x, &y, USER, NDC, dd);/* x = GConvertXUnits(REAL(label)[i], USER, NDC, dd);y = GConvertYUnits(REAL(label)[i+4], USER, NDC, dd); */if ((x < 0) || (x > 1) ||(y < 0) || (y > 1))return 1;i += 1;}return 0;}/* C o n t o u r P l o t t i n g */typedef struct SEG {struct SEG *next;double x0;double y0;double x1;double y1;} SEG, *SEGP;static SEGP *ctr_SegDB;static int ctr_intersect(double z0, double z1, double zc, double *f){if ((z0 - zc) * (z1 - zc) < 0.0) {*f = (zc - z0) / (z1 - z0);return 1;}return 0;}static SEGP ctr_newseg(double x0, double y0, double x1, double y1, SEGP prev){SEGP seg = (SEGP)R_alloc(1, sizeof(SEG));seg->x0 = x0;seg->y0 = y0;seg->x1 = x1;seg->y1 = y1;seg->next = prev;return seg;}static void ctr_swapseg(SEGP seg){double x, y;x = seg->x0;y = seg->y0;seg->x0 = seg->x1;seg->y0 = seg->y1;seg->x1 = x;seg->y1 = y;}/* Determine the entry direction to the next cell *//* and update the cell indices */#ifdef OLD#define XMATCH(x0,x1) (fabs(x0-x1)<ctr_xtol)#define YMATCH(y0,y1) (fabs(y0-y1)<ctr_ytol)#else#define XMATCH(x0,x1) (fabs(x0-x1)==0)#define YMATCH(y0,y1) (fabs(y0-y1)==0)#endifstatic double ctr_xtol;static double ctr_ytol;static int ctr_segdir(double xend, double yend, double *x, double *y,int *i, int *j, int nx, int ny){if (YMATCH(yend, y[*j])) {if (*j == 0)return 0;*j = *j - 1;return 3;}if (XMATCH(xend, x[*i])) {if (*i == 0)return 0;*i = *i - 1;return 4;}if (YMATCH(yend, y[*j + 1])) {if (*j >= ny - 1)return 0;*j = *j + 1;return 1;}if (XMATCH(xend, x[*i + 1])) {if (*i >= nx - 1)return 0;*i = *i + 1;return 2;}return 0;}/* Search seglist for a segment with endpoint (xend, yend). *//* The cell entry direction is dir, and if tail=1/0 we are *//* building the tail/head of a contour. The matching segment *//* is pointed to by seg and the updated segment list (with *//* the matched segment stripped is returned by the funtion. */static SEGP ctr_segupdate(double xend, double yend, int dir, int tail,SEGP seglist, SEGP* seg){if (seglist == NULL) {*seg = NULL;return NULL;}switch (dir) {case 1:case 3:if (YMATCH(yend,seglist->y0)) {if (!tail)ctr_swapseg(seglist);*seg = seglist;return seglist->next;}if (YMATCH(yend,seglist->y1)) {if (tail)ctr_swapseg(seglist);*seg = seglist;return seglist->next;}break;case 2:case 4:if (XMATCH(xend,seglist->x0)) {if (!tail)ctr_swapseg(seglist);*seg = seglist;return seglist->next;}if (XMATCH(xend,seglist->x1)) {if (tail)ctr_swapseg(seglist);*seg = seglist;return seglist->next;}break;}seglist->next = ctr_segupdate(xend, yend, dir, tail, seglist->next, seg);return seglist;}/* labelList, label1, and label2 are all SEXPs rather than being allocatedusing R_alloc because they need to persist across calls to contour().In do_contour() there is a vmaxget() ... vmaxset() around each call tocontour() to release all of the memory used in the drawing of thecontour _lines_ at each contour level. We need to keep track of thecontour _labels_ for _all_ contour levels, hence we have to use adifferent memory allocation mechanism.*/static SEXP labelList;staticint distFromEdge(double *xxx, double *yyy, int iii, DevDesc *dd) {return fmin2(fmin2(xxx[iii]-dd->gp.usr[0], dd->gp.usr[1]-xxx[iii]),fmin2(yyy[iii]-dd->gp.usr[2], dd->gp.usr[3]-yyy[iii]));}staticint useStart(double *xxx, double *yyy, int ns, DevDesc *dd) {if (distFromEdge(xxx, yyy, 0, dd) < distFromEdge(xxx, yyy, ns-1, dd))return 1;elsereturn 0;}staticint findGapUp(double *xxx, double *yyy, int ns, double labelDistance,DevDesc *dd) {double dX, dY;double dXC, dYC;double distanceSum = 0;int n = 0;int jjj = 1;while ((jjj < ns) && (distanceSum < labelDistance)) {/* Find a gap big enough for the labeluse several segments if necessary*/dX = xxx[jjj] - xxx[jjj - n - 1];dY = yyy[jjj] - yyy[jjj - n - 1];dXC = GConvertXUnits(dX, USER, INCHES, dd);dYC = GConvertYUnits(dY, USER, INCHES, dd);distanceSum = hypot(dXC, dYC);jjj = (jjj + 1);n += 1;}if (distanceSum < labelDistance)return 0;elsereturn n;}staticint findGapDown(double *xxx, double *yyy, int ns, double labelDistance,DevDesc *dd) {double dX, dY;double dXC, dYC;double distanceSum = 0;int n = 0;int jjj = ns - 2;while ((jjj > -1) && (distanceSum < labelDistance)) {/* Find a gap big enough for the labeluse several segments if necessary*/dX = xxx[jjj] - xxx[jjj + n + 1];dY = yyy[jjj] - yyy[jjj + n + 1];dXC = GConvertXUnits(dX, USER, INCHES, dd);dYC = GConvertYUnits(dY, USER, INCHES, dd);distanceSum = hypot(dXC, dYC);jjj--;n -= 1;}if (distanceSum < labelDistance)return 0;elsereturn -n;}static void contour(SEXP x, int nx, SEXP y, int ny, SEXP z, double zc,SEXP labels, int cnum,int drawLabels, int method, int vectorFonts, int typeface,int fontindex, double atom, DevDesc *dd){double f, xl, xh, yl, yh, zll, zhl, zlh, zhh, xx[4], yy[4];double xend, yend;int i, ii, j, jj, k, l, m, nacode, ns, ns2, dir;SEGP seglist, seg, s, start, end;double *xxx, *yyy;double variance, dX, dY, deltaX, deltaY;double dXC, dYC, deltaXC, deltaYC;int range=0, index=0, n; /* -Wall */double lowestVariance;double squareSum, sum;int iii, jjj;double distanceSum, labelDistance, avgGradient;int zeroCount;char buffer[255];double avg;int result;double ux, uy, vx, vy;double xStart, yStart;double dx, dy, dxy;double labelHeight;SEXP label1 = PROTECT(allocVector(REALSXP, 8));SEXP label2;SEXP lab;int gotLabel = 0;int ddl; /** Don't draw label */for (i = 0; i < nx - 1; i++) {xl = REAL(x)[i];xh = REAL(x)[i + 1];for (j = 0; j < ny - 1; j++) {yl = REAL(y)[j];yh = REAL(y)[j + 1];k = i + j * nx;zll = REAL(z)[k];zhl = REAL(z)[k + 1];zlh = REAL(z)[k + nx];zhh = REAL(z)[k + nx + 1];k = 0;/* If the value at a corner is *//* exactly equal to a contour *//* level, change the value at *//* corner by a tiny amount. */if (zll == zc) zll = zll + atom;if (zhl == zc) zhl = zhl + atom;if (zlh == zc) zlh = zlh + atom;if (zhh == zc) zhh = zhh + atom;/* Check for intersections with sides */nacode = 0;if (R_FINITE(zll)) nacode += 1;if (R_FINITE(zhl)) nacode += 2;if (R_FINITE(zlh)) nacode += 4;if (R_FINITE(zhh)) nacode += 8;switch (nacode) {case 15:if (ctr_intersect(zll, zhl, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yl; k++;}if (ctr_intersect(zll, zlh, zc, &f)) {yy[k] = yl + f * (yh - yl);xx[k] = xl; k++;}if (ctr_intersect(zhl, zhh, zc, &f)) {yy[k] = yl + f * (yh - yl);xx[k] = xh; k++;}if (ctr_intersect(zlh, zhh, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yh; k++;}break;case 14:if (ctr_intersect(zhl, zhh, zc, &f)) {yy[k] = yl + f * (yh - yl);xx[k] = xh; k++;}if (ctr_intersect(zlh, zhh, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yh; k++;}if (ctr_intersect(zlh, zhl, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yh + f * (yl - yh);k++;}break;case 13:if (ctr_intersect(zll, zlh, zc, &f)) {yy[k] = yl + f * (yh - yl);xx[k] = xl; k++;}if (ctr_intersect(zlh, zhh, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yh; k++;}if (ctr_intersect(zll, zhh, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yl + f * (yh - yl);k++;}break;case 11:if (ctr_intersect(zhl, zhh, zc, &f)) {yy[k] = yl + f * (yh - yl);xx[k] = xh; k++;}if (ctr_intersect(zll, zhl, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yl; k++;}if (ctr_intersect(zll, zhh, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yl + f * (yh - yl);k++;}break;case 7:if (ctr_intersect(zll, zlh, zc, &f)) {yy[k] = yl + f * (yh - yl);xx[k] = xl; k++;}if (ctr_intersect(zll, zhl, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yl; k++;}if (ctr_intersect(zlh, zhl, zc, &f)) {xx[k] = xl + f * (xh - xl);yy[k] = yh + f * (yl - yh);k++;}break;}/* We now have k(=2,4) endpoints *//* Decide which to join */seglist = NULL;if (k > 0) {if (k == 2) {seglist = ctr_newseg(xx[0], yy[0], xx[1], yy[1], seglist);}else if (k == 4) {for (k = 3; k >= 1; k--) {m = k;xl = xx[k];for (l = 0; l < k; l++) {if (xx[l] > xl) {xl = xx[l];m = l;}}if (m != k) {xl = xx[k];yl = yy[k];xx[k] = xx[m];yy[k] = yy[m];xx[m] = xl;yy[m] = yl;}}seglist = ctr_newseg(xx[0], yy[0], xx[1], yy[1], seglist);seglist = ctr_newseg(xx[2], yy[2], xx[3], yy[3], seglist);}else error("k != 2 or 4");}ctr_SegDB[i + j * nx] = seglist;}}/* The segment database is now assembled. *//* Begin following contours. *//* 1. Grab a segment *//* 2. Follow its tail *//* 3. Follow its head *//* 4. Draw the contour */for (i = 0; i < nx - 1; i++)for (j = 0; j < ny - 1; j++) {while ((seglist = ctr_SegDB[i + j * nx])) {ii = i; jj = j;start = end = seglist;ctr_SegDB[i + j * nx] = seglist->next;xend = seglist->x1;yend = seglist->y1;while ((dir = ctr_segdir(xend, yend, REAL(x), REAL(y),&ii, &jj, nx, ny))) {ctr_SegDB[ii + jj * nx]= ctr_segupdate(xend, yend, dir, 1,ctr_SegDB[ii + jj * nx], &seg);if (!seg) break;end->next = seg;end = seg;xend = end->x1;yend = end->y1;}ii = i; jj = j;xend = seglist->x0;yend = seglist->y0;while ((dir = ctr_segdir(xend, yend, REAL(x), REAL(y),&ii, &jj, nx, ny))) {ctr_SegDB[ii + jj * nx]= ctr_segupdate(xend, yend, dir, 0,ctr_SegDB[ii+jj*nx], &seg);if (!seg) break;seg->next = start;start = seg;xend = start->x0;yend = start->y0;}s = start;ns = 0;while (s) {ns++;s = s->next;}/* countour midpoint *//* use for labelling sometime */if (ns > 3) ns2 = ns/2;else ns2 = -1;s = start;xxx = (double *) C_alloc(ns + 1, sizeof(double));yyy = (double *) C_alloc(ns + 1, sizeof(double));ns = 0;xxx[ns] = s->x0;yyy[ns++] = s->y0;while (s->next) {s = s->next;xxx[ns] = s->x0;yyy[ns++] = s->y0;}xxx[ns] = s->x1;yyy[ns++] = s->y1;GMode(1, dd);/* If user supplied labels, use i'th one of themOtherwise stringify the z-value of the contour */buffer[0] = ' ';if (!isNull(labels)) {int numl = length(labels);strcpy(&buffer[1], CHAR(STRING_ELT(labels, cnum % numl)));}else {PROTECT(lab = allocVector(REALSXP, 1));REAL(lab)[0] = zc;lab = labelformat(lab);strcpy(&buffer[1], CHAR(STRING_ELT(lab, 0)));UNPROTECT(1);}buffer[strlen(buffer)+1] = '\0';buffer[strlen(buffer)] = ' ';if (vectorFonts) {/* 1, 1 => sans serif, basic font */labelDistance = GVStrWidth(buffer, typeface, fontindex,INCHES, dd);labelHeight = GVStrHeight(buffer, typeface, fontindex,INCHES, dd);} else {labelDistance = GStrWidth(buffer, INCHES, dd);labelHeight = GStrHeight(buffer, INCHES, dd);}if ((drawLabels == 1) && (labelDistance > 0)) {/* Try to find somewhere to draw the label */switch (method) {case 0: /* draw label at one end of contouroverwriting contour line*/if (useStart(xxx, yyy, ns, dd) )index = 0;elseindex = ns - 1;break;case 1: /* draw label at one end of contourembedded in contourno overlapping labels*/index = 0;range = 0;gotLabel = 0;if (useStart(xxx, yyy, ns, dd)) {iii = 0;n = findGapUp(xxx, yyy, ns, labelDistance, dd);}else {n = findGapDown(xxx, yyy, ns, labelDistance, dd);iii = ns - n - 1;}if (n > 0) {/** Find 4 corners of label extents **/FindCorners(labelDistance, labelHeight, label1,xxx[iii], yyy[iii],xxx[iii+n], yyy[iii+n], dd);/** Test corners for intersection with previous labels **/label2 = labelList;result = 0;while ((result == 0) && (label2 != R_NilValue)) {result = TestLabelIntersection(label1, CAR(label2));label2 = CDR(label2);}if (result == 0) {result = LabelInsideWindow(label1, dd);if (result == 0) {index = iii;range = n;gotLabel = 1;}}}break;case 2: /* draw label on flattest portion of contourembedded in contour lineno overlapping labels*//* Look for flatest sequence of contour gradients */lowestVariance = 9999999; /* A large number */index = 0;range = 0;gotLabel = 0;for (iii = 0; iii < ns; iii++) {distanceSum = 0;avgGradient = 0;squareSum = 0;sum = 0;n = 0;zeroCount = 0;jjj = (iii + 1);while ((jjj < ns-1) &&(distanceSum < labelDistance)) {/* Find a gap big enough for the labeluse several segments if necessary*/dX = xxx[jjj] - xxx[jjj - n - 1];dY = yyy[jjj] - yyy[jjj - n - 1];dXC = GConvertXUnits(dX, USER, INCHES, dd);dYC = GConvertYUnits(dY, USER, INCHES, dd);distanceSum = hypot(dXC, dYC);/* Calculate the variance of the gradientsof the segments that will make way for thelabel*/deltaX = xxx[jjj] - xxx[jjj - 1];deltaY = yyy[jjj] - yyy[jjj - 1];deltaXC = GConvertXUnits(deltaX, USER, INCHES, dd);deltaYC = GConvertYUnits(deltaY, USER, INCHES, dd);if (deltaX == 0) {deltaX = 1;}avgGradient += (deltaY/deltaX);squareSum += avgGradient * avgGradient;jjj = (jjj + 1);n += 1;}if (distanceSum < labelDistance)break;/** Find 4 corners of label extents **/FindCorners(labelDistance, labelHeight, label1,xxx[iii], yyy[iii],xxx[iii+n], yyy[iii+n], dd);/** Test corners for intersection with previous labels **/label2 = labelList;result = 0;while ((result == 0) && (label2 != R_NilValue)) {result = TestLabelIntersection(label1, CAR(label2));label2 = CDR(label2);}if (result == 0)result = LabelInsideWindow(label1, dd);if (result == 0) {variance = (squareSum - (avgGradient * avgGradient) / n) / n;avgGradient /= n;if (variance < lowestVariance) {lowestVariance = variance;index = iii;range = n;avg = avgGradient;}}if (lowestVariance < 9999999)gotLabel = 1;}} /* switch (method) */if (method == 0) {GPolyline(ns, xxx, yyy, USER, dd);if (vectorFonts)GVText(xxx[index], yyy[index], USER, buffer,typeface, fontindex,.5, .5, 0, dd);elseGText(xxx[index], yyy[index], USER, buffer,.5, .5, 0, dd);} else {for (iii = 0; iii < index; iii++)GLine(xxx[iii], yyy[iii],xxx[iii+1], yyy[iii+1], USER, dd);for (iii = index+range; iii < ns - 1; iii++)GLine(xxx[iii], yyy[iii],xxx[iii+1], yyy[iii+1], USER, dd);if (gotLabel) {/* find which plot edge we are closest to */int closest; /* 0 = index, 1 = index+range */double dx1, dx2, dy1, dy2, dmin;dx1 = fmin2((xxx[index] - dd->gp.usr[0]),(dd->gp.usr[1] - xxx[index]));dx2 = fmin2((dd->gp.usr[1] - xxx[index+range]),(xxx[index+range] - dd->gp.usr[0]));if (dx1 < dx2) {closest = 0;dmin = dx1;} else {closest = 1;dmin = dx2;}dy1 = fmin2((yyy[index] - dd->gp.usr[2]),(dd->gp.usr[3] - yyy[index]));if (closest && (dy1 < dmin)) {closest = 0;dmin = dy1;} else if (dy1 < dmin)dmin = dy1;dy2 = fmin2((dd->gp.usr[3] - yyy[index+range]),(yyy[index+range] - dd->gp.usr[2]));if (!closest && (dy2 < dmin))closest = 1;dx = GConvertXUnits(xxx[index+range] - xxx[index],USER, INCHES, dd);dy = GConvertYUnits(yyy[index+range] - yyy[index],USER, INCHES, dd);dxy = hypot(dx, dy);/* save the current label for checking overlap */label2 = allocVector(REALSXP, 8);FindCorners(labelDistance, labelHeight, label2,xxx[index], yyy[index],xxx[index+range], yyy[index+range], dd);UNPROTECT_PTR(labelList);labelList = PROTECT(CONS(label2, labelList));ddl = 0;/* draw an extra bit of segment if the labeldoesn't fill the gap */if (closest) {xStart = xxx[index+range] -(xxx[index+range] - xxx[index]) *labelDistance / dxy;yStart = yyy[index+range] -(yyy[index+range] - yyy[index]) *labelDistance / dxy;if (labelDistance / dxy < 1)GLine(xxx[index], yyy[index],xStart, yStart,USER, dd);} else {xStart = xxx[index] +(xxx[index+range] - xxx[index]) *labelDistance / dxy;yStart = yyy[index] +(yyy[index+range] - yyy[index]) *labelDistance / dxy;if (labelDistance / dxy < 1)GLine(xStart, yStart,xxx[index+range], yyy[index+range],USER, dd);}/*** Draw contour labels ***/if (xxx[index] < xxx[index+range]) {if (closest) {ux = xStart;uy = yStart;vx = xxx[index+range];vy = yyy[index+range];} else {ux = xxx[index];uy = yyy[index];vx = xStart;vy = yStart;}}else {if (closest) {ux = xxx[index+range];uy = yyy[index+range];vx = xStart;vy = yStart;} else {ux = xStart;uy = yStart;vx = xxx[index];vy = yyy[index];}}if (ddl == 0) {/* convert to INCHES for calculation ofangle to draw text*/GConvert(&ux, &uy, USER, INCHES, dd);GConvert(&vx, &vy, USER, INCHES, dd);/* 1, 1 => sans serif, basic font0, .5 => left, centre justified */if (vectorFonts)GVText(ux, uy, INCHES, buffer,typeface, fontindex,0, .5,(180 / 3.14) *atan2(vy - uy, vx - ux),dd);elseGText(ux, uy, INCHES, buffer, 0, .5,(180 / 3.14) *atan2(vy - uy, vx - ux),dd);}} /* if (gotLabel) */} /* if (method == 0) else ... */} /* if ((drawLabels == 1) && (labelDistance > 0)) */else {GPolyline(ns, xxx, yyy, USER, dd);}GMode(0, dd);C_free((char *) xxx);C_free((char *) yyy);}}UNPROTECT_PTR(label1); /* pwwwargh! This is messy, but last thingprotected is likely labelList, and that needsto be preserved across calls */}/* contour(x,y,z, levels, col, lty) */SEXP do_contour(SEXP call, SEXP op, SEXP args, SEXP env){SEXP oargs, c, x, y, z, vfont, col, lty, lwd, labels;int i, j, nx, ny, nc, ncol, nlty, nlwd;int ltysave, colsave, lwdsave;double cexsave;double atom, zmin, zmax;char *vmax, *vmax0;int drawLabels;int method;int vectorFonts = 0;int typeface = 0;int fontindex = 0;double labcex;DevDesc *dd = CurrentDevice();GCheckState(dd);if (length(args) < 4)errorcall(call, "too few arguments");oargs = args;x = CAR(args);internalTypeCheck(call, x, REALSXP);nx = LENGTH(x);args = CDR(args);y = CAR(args);internalTypeCheck(call, y, REALSXP);ny = LENGTH(y);args = CDR(args);z = CAR(args);internalTypeCheck(call, z, REALSXP);args = CDR(args);c = CAR(args);internalTypeCheck(call, c, REALSXP);nc = LENGTH(c);args = CDR(args);labels = CAR(args);if (!isNull(labels))internalTypeCheck(call, labels, STRSXP);args = CDR(args);labcex = asReal(CAR(args));args = CDR(args);drawLabels = asLogical(CAR(args));args = CDR(args);method = asInteger(CAR(args)); args = CDR(args);if (method < 1 || method > 3)errorcall(call, "invalid value for \"method\"");PROTECT(vfont = FixupVFont(CAR(args)));if (!isNull(vfont)) {vectorFonts = 1;typeface = INTEGER(vfont)[0];fontindex = INTEGER(vfont)[1];}args = CDR(args);PROTECT(col = FixupCol(CAR(args), NA_INTEGER));ncol = length(col);args = CDR(args);PROTECT(lty = FixupLty(CAR(args), dd->gp.lty));nlty = length(lty);args = CDR(args);PROTECT(lwd = FixupLwd(CAR(args), dd->gp.lwd));nlwd = length(lwd);args = CDR(args);if (nx < 2 || ny < 2)errorcall(call, "insufficient x or y values");if (nrows(z) != nx || ncols(z) != ny)errorcall(call, "dimension mismatch");if (nc < 1)errorcall(call, "no contour values");for (i = 0; i < nx; i++) {if (!R_FINITE(REAL(x)[i]))errorcall(call, "missing x values");if (i > 0 && REAL(x)[i] < REAL(x)[i - 1])errorcall(call, "increasing x values expected");}for (i = 0; i < ny; i++) {if (!R_FINITE(REAL(y)[i]))errorcall(call, "missing y values");if (i > 0 && REAL(y)[i] < REAL(y)[i - 1])errorcall(call, "increasing y values expected");}ctr_xtol = 1e-3 * fabs(REAL(x)[nx-1]-REAL(x)[0]);ctr_ytol = 1e-3 * fabs(REAL(y)[ny-1]-REAL(y)[0]);for (i = 0; i < nc; i++)if (!R_FINITE(REAL(c)[i]))errorcall(call, "illegal NA contour values");zmin = DBL_MAX;zmax = DBL_MIN;for (i = 0; i < nx * ny; i++)if (R_FINITE(REAL(z)[i])) {if (zmax < REAL(z)[i]) zmax = REAL(z)[i];if (zmin > REAL(z)[i]) zmin = REAL(z)[i];}if (zmin >= zmax) {if (zmin == zmax)warning("all z values are equal");elsewarning("all z values are NA");return R_NilValue;}/* PREVIOUSLY: atom = DBL_EPSILON * (zmax - zmin); */atom = 1e-3 * (zmax - zmin);/* Initialize the segment data base *//* Note we must be careful about resetting *//* the top of the stack, otherwise we run out of *//* memory after a sequence of displaylist replays */vmax0 = vmaxget();ctr_SegDB = (SEGP*)R_alloc(nx*ny, sizeof(SEGP));for (i = 0; i < nx; i++)for (j = 0; j < ny; j++)ctr_SegDB[i + j * nx] = NULL;/* Draw the contours -- note the heap release */ltysave = dd->gp.lty;colsave = dd->gp.col;lwdsave = dd->gp.lwd;cexsave = dd->gp.cex;labelList = PROTECT(R_NilValue);GMode(1, dd);for (i = 0; i < nc; i++) {vmax = vmaxget();dd->gp.lty = INTEGER(lty)[i % nlty];if (dd->gp.lty == NA_INTEGER)dd->gp.lty = ltysave;dd->gp.col = INTEGER(col)[i % ncol];if (dd->gp.col == NA_INTEGER)dd->gp.col = colsave;dd->gp.lwd = REAL(lwd)[i % nlwd];if (dd->gp.lwd == NA_REAL)dd->gp.lwd = lwdsave;dd->gp.cex = labcex;contour(x, nx, y, ny, z, REAL(c)[i], labels, i,drawLabels, method-1,vectorFonts, typeface, fontindex, atom, dd);vmaxset(vmax);}GMode(0, dd);vmaxset(vmax0);dd->gp.lty = ltysave;dd->gp.col = colsave;dd->gp.lwd = lwdsave;dd->gp.cex = cexsave;UNPROTECT(5);/* NOTE: only record operation if no "error" *//* NOTE: on replay, call == R_NilValue */if (call != R_NilValue)recordGraphicOperation(op, oargs, dd);return R_NilValue;}/* F i l l e d C o n t o u r P l o t s *//* R o s s I h a k a, M a r c h 1 9 9 9 */static voidFindCutPoints(double low, double high,double x1, double y1, double z1,double x2, double y2, double z2,double *x, double *y, double *z,int *npt){double c;if (z1 > z2 ) {if (z2 > high || z1 < low)return;if (z1 < high) {x[*npt] = x1;y[*npt] = y1;z[*npt] = z1;++*npt;}else {c = (z1 - high) / (z1 - z2);x[*npt] = x1 + c * (x2 - x1);y[*npt] = y1;z[*npt] = z1 + c * (z2 - z1);++*npt;}if (z2 > low) {#ifdef OMIT/* Don't repeat corner vertices */x[*npt] = x2;y[*npt] = y2;z[*npt] = z2;++*npt;#endif}else {c = (z2 -low) / (z2 - z1);x[*npt] = x2 - c * (x2 - x1);y[*npt] = y1;z[*npt] = z2 - c * (z2 - z1);++*npt;}}else if (z1 < z2) {if (z2 < low || z1 > high)return;if (z1 > low) {x[*npt] = x1;y[*npt] = y1;z[*npt] = z1;++*npt;}else {c = (z1 - low) / (z1 - z2);x[*npt] = x1 + c * (x2 - x1);y[*npt] = y1;z[*npt] = z1 + c * (z2 - z1);++*npt;}if (z2 < high) {#ifdef OMIT/* Don't repeat corner vertices */x[*npt] = x2;y[*npt] = y2;z[*npt] = z2;++*npt;#endif}else {c = (z2 - high) / (z2 - z1);x[*npt] = x2 - c * (x2 - x1);y[*npt] = y1;z[*npt] = z2 - c * (z2 - z1);++*npt;}}else {if(low <= z1 && z1 <= high) {x[*npt] = x1;y[*npt] = y1;z[*npt] = z1;++*npt;#ifdef OMIT/* Don't repeat corner vertices */x[*npt] = x2;y[*npt] = y2;z[*npt] = z2;++*npt;#endif}}}/* FIXME - This could pretty easily be adapted to handle NA *//* values on the grid. Just search the diagonals for cutpoints *//* instead of the cell sides. Use the same switch idea as in *//* contour above. There are 5 cases to handle. */static voidFindPolygonVertices(double low, double high,double x1, double x2, double y1, double y2,double z11, double z21, double z12, double z22,double *x, double *y, double *z, int *npt){*npt = 0;FindCutPoints(low, high, x1, y1, z11, x2, y1, z21, x, y, z, npt);FindCutPoints(low, high, y1, x2, z21, y2, x2, z22, y, x, z, npt);FindCutPoints(low, high, x2, y2, z22, x1, y2, z12, x, y, z, npt);FindCutPoints(low, high, y2, x1, z12, y1, x1, z11, y, x, z, npt);}/* FIXME: [Code consistency] Use macro for the parallel parts ofdo_contour, do_filledcontour & do_image ...*/SEXP do_filledcontour(SEXP call, SEXP op, SEXP args, SEXP env){SEXP oargs, sx, sy, sz, sc, scol;double *x, *y, *z, *c;unsigned *col;int i, j, k, npt, nx, ny, nz, nc, ncol, colsave, xpdsave;double px[8], py[8], pz[8];DevDesc *dd = CurrentDevice();GCheckState(dd);checkArity(op,args);oargs = args;sx = CAR(args);internalTypeCheck(call, sx, REALSXP);nx = LENGTH(sx);args = CDR(args);sy = CAR(args);internalTypeCheck(call, sy, REALSXP);ny = LENGTH(sy);args = CDR(args);sz = CAR(args);internalTypeCheck(call, sz, REALSXP);nz = length(sz);args = CDR(args);sc = CAR(args);internalTypeCheck(call, sc, REALSXP);nc = length(sc);args = CDR(args);PROTECT(scol = FixupCol(CAR(args), NA_INTEGER));ncol = length(scol);/* Shorthand Pointers */x = REAL(sx);y = REAL(sy);z = REAL(sz);c = REAL(sc);col = (unsigned*)INTEGER(scol);/* Check of grid coordinates *//* We want them to all be finite *//* and in strictly ascending order */if (nx < 1 || ny < 1) goto badxy;if (!R_FINITE(x[0])) goto badxy;if (!R_FINITE(y[0])) goto badxy;for (i = 1; i < nx; i++)if (!R_FINITE(x[i]) || x[i] <= x[i - 1]) goto badxy;for (j = 1; j < ny; j++)if (!R_FINITE(y[j]) || y[j] <= y[j - 1]) goto badxy;/* Check of the contour levels */if (!R_FINITE(c[0])) goto badlev;for (k = 1; k < nc; k++)if (!R_FINITE(c[k]) || c[k] <= c[k - 1]) goto badlev;colsave = dd->gp.col;xpdsave = dd->gp.xpd;/* override par("xpd") and force clipping to plot region */dd->gp.xpd = 0;GMode(1, dd);for (i = 1; i < nx; i++) {for (j = 1; j < ny; j++) {for (k = 1; k < nc ; k++) {FindPolygonVertices(c[k - 1], c[k],x[i - 1], x[i],y[j - 1], y[j],z[i - 1 + (j - 1) * nx],z[i + (j - 1) * nx],z[i - 1 + j * nx],z[i + j * nx],px, py, pz, &npt);if (npt > 2)GPolygon(npt, px, py, USER, col[(k-1)%ncol],NA_INTEGER, dd);}}}GMode(0, dd);dd->gp.col = colsave;dd->gp.xpd = xpdsave;R_Visible = 0;UNPROTECT(1);if (call != R_NilValue)recordGraphicOperation(op, oargs, dd);return R_NilValue;badxy:errorcall(call, "invalid x / y values or limits");badlev:errorcall(call, "invalid contour levels");return R_NilValue; /* never used; to keep -Wall happy */}/* I m a g e R e n d e r i n g *//* image(x, y, z, col, breaks) */SEXP do_image(SEXP call, SEXP op, SEXP args, SEXP env){SEXP oargs, sx, sy, sz, sc;double *x, *y;int *z, tmp;unsigned *c;int i, j, nx, ny, nc, colsave, xpdsave;DevDesc *dd = CurrentDevice();GCheckState(dd);checkArity(op,args);oargs = args;sx = CAR(args);internalTypeCheck(call, sx, REALSXP);nx = LENGTH(sx);args = CDR(args);sy = CAR(args);internalTypeCheck(call, sy, REALSXP);ny = LENGTH(sy);args = CDR(args);sz = CAR(args);internalTypeCheck(call, sz, INTSXP);args = CDR(args);PROTECT(sc = FixupCol(CAR(args), NA_INTEGER));nc = LENGTH(sc);/* Shorthand Pointers */x = REAL(sx);y = REAL(sy);z = INTEGER(sz);c = (unsigned*)INTEGER(sc);/* Check of grid coordinates *//* We want them to all be finite and in strictly ascending order */if (nx < 1 || ny < 1) goto badxy;if (!R_FINITE(x[0])) goto badxy;if (!R_FINITE(y[0])) goto badxy;for (i = 1; i < nx; i++)if (!R_FINITE(x[i]) || x[i] <= x[i - 1]) goto badxy;for (j = 1; j < ny; j++)if (!R_FINITE(y[j]) || y[j] <= y[j - 1]) goto badxy;colsave = dd->gp.col;xpdsave = dd->gp.xpd;/* override par("xpd") and force clipping to plot region */dd->gp.xpd = 0;GMode(1, dd);for (i = 0; i < nx - 1 ; i++) {for (j = 0; j < ny - 1; j++) {tmp = z[i + j * (nx - 1)];if (tmp >= 0 && tmp < nc && tmp != NA_INTEGER)GRect(x[i], y[j], x[i+1], y[j+1], USER, c[tmp],NA_INTEGER, dd);}}GMode(0, dd);dd->gp.col = colsave;dd->gp.xpd = xpdsave;R_Visible = 0;UNPROTECT(1);if (call != R_NilValue)recordGraphicOperation(op, oargs, dd);return R_NilValue;badxy:errorcall(call, "invalid x / y values or limits");return R_NilValue;/* never used; to keep -Wall happy */}/* P e r s p e c t i v e S u r f a c e P l o t s */#ifdef NOT_used_currently/*-- out 'def' (-Wall) --*/static void MakeVector (double x, double y, double z, Vector3d v){v[0] = x;v[1] = y;v[2] = z;v[3] = 1;}#endif/* Set up the light source */static double Light[4];static double Shade;static int DoLighting;static void SetUpLight(double theta, double phi){double u[4];u[0] = 0; u[1] = -1; u[2] = 0; u[3] = 1;SetToIdentity(VT); /* Initialization */XRotate(-phi); /* colatitude rotation */ZRotate(theta); /* azimuthal rotation */TransVector(u, VT, Light); /* transform */}static double FacetShade(double *u, double *v){double nx, ny, nz, sum;nx = u[1] * v[2] - u[2] * v[1];ny = u[2] * v[0] - u[0] * v[2];nz = u[0] * v[1] - u[1] * v[0];sum = sqrt(nx * nx + ny * ny + nz * nz);if (sum == 0) sum = 1;nx /= sum;ny /= sum;nz /= sum;sum = 0.5 * (nx * Light[0] + ny * Light[1] + nz * Light[2] + 1);return pow(sum, Shade);}/* For each facet, determine the farthest point from the eye. *//* Sorting the facets so that these depths are decreasing *//* yields an occlusion compatible ordering. *//* Note that we ignore z values when doing this. */static void DepthOrder(double *z, double *x, double *y, int nx, int ny,double *depth, int *index){int i, ii, j, jj, nx1, ny1;Vector3d u, v;double d;nx1 = nx - 1;ny1 = ny - 1;for (i = 0; i < nx1 * ny1; i++)index[i] = i;for (i = 0; i < nx1; i++)for (j = 0; j < ny1; j++) {d = -DBL_MAX;for (ii = 0; ii <= 1; ii++)for (jj = 0; jj <= 1; jj++) {u[0] = x[i + ii];u[1] = y[j + jj];/* Originally I had the following line here: *//* u[2] = z[i+ii+(j+jj)*nx]; *//* But this leads to artifacts. *//* It has been replaced by the following line: */u[2] = 0;u[3] = 1;if (R_FINITE(u[0]) && R_FINITE(u[1]) && R_FINITE(u[2])) {TransVector(u, VT, v);if (v[3] > d) d = v[3];}}depth[i+j*nx1] = -d;}/* Determine the depth ordering of the facets to ensurethat they are drawn in an occlusion compatible order. */rsort_with_index(depth, index, nx1 * ny1);}static void DrawFacets(double *z, double *x, double *y, int nx, int ny,int *index, double xs, double ys, double zs,int *col, int ncol, int border){double xx[4], yy[4], shade = 0;Vector3d u, v;int i, j, k, n, nx1, ny1, icol, nv;unsigned int newcol, r, g, b;DevDesc *dd;dd = CurrentDevice();nx1 = nx - 1;ny1 = ny - 1;n = nx1 * ny1;for (k = 0; k < n; k++) {nv = 0;i = index[k] % nx1;j = index[k] / nx1;icol = (i + j * nx1) % ncol;if (DoLighting) {/* Note we must scale here */u[0] = xs * (x[i+1] - x[i]);u[1] = ys * (y[j] - y[j+1]);u[2] = zs * (z[(i+1)+j*nx] - z[i+(j+1)*nx]);v[0] = xs * (x[i+1] - x[i]);v[1] = ys * (y[j+1] - y[j]);v[2] = zs * (z[(i+1)+(j+1)*nx] - z[i+j*nx]);shade = FacetShade(u, v);}u[0] = x[i]; u[1] = y[j];u[2] = z[i + j * nx]; u[3] = 1;if (R_FINITE(u[0]) && R_FINITE(u[1]) && R_FINITE(u[2])) {TransVector(u, VT, v);xx[nv] = v[0] / v[3];yy[nv] = v[1] / v[3];nv++;}u[0] = x[i + 1]; u[1] = y[j];u[2] = z[i + 1 + j * nx]; u[3] = 1;if (R_FINITE(u[0]) && R_FINITE(u[1]) && R_FINITE(u[2])) {TransVector(u, VT, v);xx[nv] = v[0] / v[3];yy[nv] = v[1] / v[3];nv++;}u[0] = x[i + 1]; u[1] = y[j + 1];u[2] = z[i + 1 + (j + 1) * nx]; u[3] = 1;if (R_FINITE(u[0]) && R_FINITE(u[1]) && R_FINITE(u[2])) {TransVector(u, VT, v);xx[nv] = v[0] / v[3];yy[nv] = v[1] / v[3];nv++;}u[0] = x[i]; u[1] = y[j + 1];u[2] = z[i + (j + 1) * nx]; u[3] = 1;if (R_FINITE(u[0]) && R_FINITE(u[1]) && R_FINITE(u[2])) {TransVector(u, VT, v);xx[nv] = v[0] / v[3];yy[nv] = v[1] / v[3];nv++;}if (nv > 2) {newcol = col[icol];if (DoLighting) {r = shade * R_RED(newcol);g = shade * R_GREEN(newcol);b = shade * R_BLUE(newcol);newcol = R_RGB(r, g, b);}GPolygon(nv, xx, yy, USER, newcol, border, dd);}}}#ifdef NOT_used_currently/*-- out 'def' (-Wall) --*/static void CheckRange(double *x, int n, double min, double max){double xmin, xmax;int i;xmin = DBL_MAX;xmax = -DBL_MAX;for (i = 0; i < n; i++)if (R_FINITE(x[i])) {if (x[i] < xmin) xmin = x[i];if (x[i] > xmax) xmax = x[i];}if (xmin < min || xmax > max)errorcall(gcall, "coordinates outsize specified range");}#endifstatic void PerspWindow(double *xlim, double *ylim, double *zlim, DevDesc *dd){double pin1, pin2, scale, xdelta, ydelta, xscale, yscale, xadd, yadd;double xmax, xmin, ymax, ymin, xx, yy;Vector3d u, v;int i, j, k;xmax = xmin = ymax = ymin = 0;u[3] = 1;for (i = 0; i < 2; i++) {u[0] = xlim[i];for (j = 0; j < 2; j++) {u[1] = ylim[j];for (k = 0; k < 2; k++) {u[2] = zlim[k];TransVector(u, VT, v);xx = v[0] / v[3];yy = v[1] / v[3];if (xx > xmax) xmax = xx;if (xx < xmin) xmin = xx;if (yy > ymax) ymax = yy;if (yy < ymin) ymin = yy;}}}pin1 = GConvertXUnits(1.0, NPC, INCHES, dd);pin2 = GConvertYUnits(1.0, NPC, INCHES, dd);xdelta = fabs(xmax - xmin);ydelta = fabs(ymax - ymin);xscale = pin1 / xdelta;yscale = pin2 / ydelta;scale = (xscale < yscale) ? xscale : yscale;xadd = .5 * (pin1 / scale - xdelta);yadd = .5 * (pin2 / scale - ydelta);GScale(xmin - xadd, xmax + xadd, 1, dd);GScale(ymin - yadd, ymax + yadd, 2, dd);GMapWin2Fig(dd);}static int LimitCheck(double *lim, double *c, double *s){if (!R_FINITE(lim[0]) || !R_FINITE(lim[1]) || lim[0] >= lim[1])return 0;*s = 0.5 * fabs(lim[1] - lim[0]);*c = 0.5 * (lim[1] + lim[0]);return 1;}/* PerspBox: The following code carries out a visibility test *//* on the surfaces of the xlim/ylim/zlim box around the plot. *//* If front = 0, only the faces with their inside toward the *//* eyepoint are drawn. If front = 1, only the faces with *//* their outside toward the eye are drawn. This lets us carry *//* out hidden line removal by drawing any faces which will be *//* obscured before the surface, and those which will not be *//* obscured after the surface. *//* The vertices of the box */static short int Vertex[8][3] = {{0, 0, 0},{0, 0, 1},{0, 1, 0},{0, 1, 1},{1, 0, 0},{1, 0, 1},{1, 1, 0},{1, 1, 1},};/* The vertices visited when tracing a face */static short int Face[6][4] = {{0, 1, 5, 4},{2, 6, 7, 3},{0, 2, 3, 1},{4, 5, 7, 6},{0, 4, 6, 2},{1, 3, 7, 5},};/* The edges drawn when tracing a face */static short int Edge[6][4] = {{ 0, 1, 2, 3},{ 4, 5, 6, 7},{ 8, 7, 9, 0},{ 2,10, 5,11},{ 3,11, 4, 8},{ 9, 6,10, 1},};/* Which edges have been drawn previously */static char EdgeDone[12];static void PerspBox(int front, double *x, double *y, double *z, DevDesc *dd){Vector3d u0, v0, u1, v1, u2, v2, u3, v3;double d[3], e[3];int f, i, p0, p1, p2, p3, nearby;int ltysave = dd->gp.lty;if (front)dd->gp.lty = LTY_DOTTED;elsedd->gp.lty = LTY_SOLID;for (f = 0; f < 6; f++) {p0 = Face[f][0];p1 = Face[f][1];p2 = Face[f][2];p3 = Face[f][3];u0[0] = x[Vertex[p0][0]];u0[1] = y[Vertex[p0][1]];u0[2] = z[Vertex[p0][2]];u0[3] = 1;u1[0] = x[Vertex[p1][0]];u1[1] = y[Vertex[p1][1]];u1[2] = z[Vertex[p1][2]];u1[3] = 1;u2[0] = x[Vertex[p2][0]];u2[1] = y[Vertex[p2][1]];u2[2] = z[Vertex[p2][2]];u2[3] = 1;u3[0] = x[Vertex[p3][0]];u3[1] = y[Vertex[p3][1]];u3[2] = z[Vertex[p3][2]];u3[3] = 1;TransVector(u0, VT, v0);TransVector(u1, VT, v1);TransVector(u2, VT, v2);TransVector(u3, VT, v3);/* Visibility test. *//* Determine whether the surface normal is toward the eye. *//* Note that we only draw lines once. */for (i = 0; i < 3; i++) {d[i] = v1[i]/v1[3] - v0[i]/v0[3];e[i] = v2[i]/v2[3] - v1[i]/v1[3];}nearby = (d[0]*e[1] - d[1]*e[0]) < 0;if ((front && nearby) || (!front && !nearby)) {if (!EdgeDone[Edge[f][0]]++)GLine(v0[0]/v0[3], v0[1]/v0[3],v1[0]/v1[3], v1[1]/v1[3], USER, dd);if (!EdgeDone[Edge[f][1]]++)GLine(v1[0]/v1[3], v1[1]/v1[3],v2[0]/v2[3], v2[1]/v2[3], USER, dd);if (!EdgeDone[Edge[f][2]]++)GLine(v2[0]/v2[3], v2[1]/v2[3],v3[0]/v3[3], v3[1]/v3[3], USER, dd);if (!EdgeDone[Edge[f][3]]++)GLine(v3[0]/v3[3], v3[1]/v3[3],v0[0]/v0[3], v0[1]/v0[3], USER, dd);}}dd->gp.lty = ltysave;}/* PerspAxes:*//* Starting vertex for possible axes */static short int AxisStart[8] = { 0, 0, 2, 4, 0, 4, 2, 6 };/* Tick vector for possible axes */static short int TickVector[8][3] = {{0, -1, -1},{-1, 0, -1},{0, 1, -1},{1, 0, -1},{-1, -1, 0},{1, -1, 0},{-1, 1, 0},{1, 1, 0}};static int lowest(double y1, double y2, double y3, double y4) {return ((y1 <= y2) && (y1 <= y3) && (y1 <= y4));}static double labelAngle(double x1, double y1, double x2, double y2) {double dx, dy;double angle;dx = fabs(x2 - x1);if (x2 > x1)dy = y2 - y1;elsedy = y1 - y2;if (dx == 0) {if (dy > 0)angle = 90;elseangle = 270;} else {angle = (180 / M_PI) * atan2(dy, dx);}return angle;}static void PerspAxis(double *x, double *y, double *z,int axis, int axisType, int nTicks, int tickType,char *label, DevDesc *dd) {Vector3d u1, u2, u3, v1, v2, v3;double tickLength = .03; /* proportion of axis length */double min, max;double *range = NULL; /* -Wall */double axp[3];int nint, i;SEXP at, lab;switch (axisType) {case 0:min = x[0];max = x[1];range = x;break;case 1:min = y[0];max = y[1];range = y;break;case 2:min = z[0];max = z[1];range = z;break;}nint = nTicks-1;GPretty(&min, &max, &nint);axp[0] = min;axp[1] = max;axp[2] = nint;/* Do the following calculations for both ticktypes */switch (axisType) {case 0:u1[0] = min;u1[1] = y[Vertex[AxisStart[axis]][1]];u1[2] = z[Vertex[AxisStart[axis]][2]];break;case 1:u1[0] = x[Vertex[AxisStart[axis]][0]];u1[1] = min;u1[2] = z[Vertex[AxisStart[axis]][2]];break;case 2:u1[0] = x[Vertex[AxisStart[axis]][0]];u1[1] = y[Vertex[AxisStart[axis]][1]];u1[2] = min;break;}u1[0] = u1[0] + tickLength*(x[1]-x[0])*TickVector[axis][0];u1[1] = u1[1] + tickLength*(y[1]-y[0])*TickVector[axis][1];u1[2] = u1[2] + tickLength*(z[1]-z[0])*TickVector[axis][2];u1[3] = 1;switch (axisType) {case 0:u2[0] = max;u2[1] = u1[1];u2[2] = u1[2];break;case 1:u2[0] = u1[0];u2[1] = max;u2[2] = u1[2];break;case 2:u2[0] = u1[0];u2[1] = u1[1];u2[2] = max;break;}u2[3] = 1;/* The axis label has to be further out for "detailed" ticksin order to leave room for the tick labels */switch (tickType) {case 1: /* "simple": just an arrow parallel to axis, indicating directionof increase */u3[0] = u1[0] + tickLength*(x[1]-x[0])*TickVector[axis][0];u3[1] = u1[1] + tickLength*(y[1]-y[0])*TickVector[axis][1];u3[2] = u1[2] + tickLength*(z[1]-z[0])*TickVector[axis][2];break;case 2:u3[0] = u1[0] + 2.5*tickLength*(x[1]-x[0])*TickVector[axis][0];u3[1] = u1[1] + 2.5*tickLength*(y[1]-y[0])*TickVector[axis][1];u3[2] = u1[2] + 2.5*tickLength*(z[1]-z[0])*TickVector[axis][2];break;}switch (axisType) {case 0:u3[0] = (min + max)/2;break;case 1:u3[1] = (min + max)/2;break;case 2:u3[2] = (min + max)/2;break;}u3[3] = 1;TransVector(u1, VT, v1);TransVector(u2, VT, v2);TransVector(u3, VT, v3);/* Draw axis label */GText(v3[0]/v3[3], v3[1]/v3[3], USER, label, .5, .5,labelAngle(v1[0]/v1[3], v1[1]/v1[3], v2[0]/v2[3], v2[1]/v2[3]),dd);/* Draw axis ticks */switch (tickType) {case 1: /* "simple": just an arrow parallel to axis, indicating directionof increase *//* arrow head is 0.25 inches long, with angle 30 degrees,and drawn at v2 end of line */GArrow(v1[0]/v1[3], v1[1]/v1[3],v2[0]/v2[3], v2[1]/v2[3], USER,0.1, 10, 2, dd);break;case 2: /* "detailed": normal ticks as per 2D plots */PROTECT(at = CreateAtVector(axp, range, 7, 0));PROTECT(lab = labelformat(at));for (i=0; i<length(at); i++) {switch (axisType) {case 0:u1[0] = REAL(at)[i];u1[1] = y[Vertex[AxisStart[axis]][1]];u1[2] = z[Vertex[AxisStart[axis]][2]];break;case 1:u1[0] = x[Vertex[AxisStart[axis]][0]];u1[1] = REAL(at)[i];u1[2] = z[Vertex[AxisStart[axis]][2]];break;case 2:u1[0] = x[Vertex[AxisStart[axis]][0]];u1[1] = y[Vertex[AxisStart[axis]][1]];u1[2] = REAL(at)[i];break;}u1[3] = 1;u2[0] = u1[0] + tickLength*(x[1]-x[0])*TickVector[axis][0];u2[1] = u1[1] + tickLength*(y[1]-y[0])*TickVector[axis][1];u2[2] = u1[2] + tickLength*(z[1]-z[0])*TickVector[axis][2];u2[3] = 1;u3[0] = u2[0] + tickLength*(x[1]-x[0])*TickVector[axis][0];u3[1] = u2[1] + tickLength*(y[1]-y[0])*TickVector[axis][1];u3[2] = u2[2] + tickLength*(z[1]-z[0])*TickVector[axis][2];u3[3] = 1;TransVector(u1, VT, v1);TransVector(u2, VT, v2);TransVector(u3, VT, v3);/* Draw tick line */GLine(v1[0]/v1[3], v1[1]/v1[3],v2[0]/v2[3], v2[1]/v2[3], USER, dd);/* Draw tick label */GText(v3[0]/v3[3], v3[1]/v3[3], USER, CHAR(STRING_ELT(lab, i)),.5, .5, 0, dd);}UNPROTECT(2);break;}}static void PerspAxes(double *x, double *y, double *z,char *xlab, char *ylab, char *zlab,int nTicks, int tickType, DevDesc *dd) {int xAxis=0, yAxis=0, zAxis=0; /* -Wall */int xpdsave;Vector3d u0 = {0, 0, 0, 1};Vector3d u1 = {1, 0, 0, 1};Vector3d u2 = {0, 1, 0, 1};Vector3d u3 = {1, 1, 0, 1};Vector3d v0, v1, v2, v3;TransVector(u0, VT, v0);TransVector(u1, VT, v1);TransVector(u2, VT, v2);TransVector(u3, VT, v3);/* to fit in the axis labels */xpdsave = dd->gp.xpd;dd->gp.xpd = 1;/* Figure out which X and Y axis to draw */if (lowest(v0[1]/v0[3], v1[1]/v1[3], v2[1]/v2[3], v3[1]/v3[3])) {xAxis = 0;yAxis = 1;} else if (lowest(v1[1]/v1[3], v0[1]/v0[3], v2[1]/v2[3], v3[1]/v3[3])) {xAxis = 0;yAxis = 3;} else if (lowest(v2[1]/v2[3], v1[1]/v1[3], v0[1]/v0[3], v3[1]/v3[3])) {xAxis = 2;yAxis = 1;} else if (lowest(v3[1]/v3[3], v1[1]/v1[3], v2[1]/v2[3], v0[1]/v0[3])) {xAxis = 2;yAxis = 3;} elsewarning("Axis orientation not calculated");PerspAxis(x, y, z, xAxis, 0, nTicks, tickType, xlab, dd);PerspAxis(x, y, z, yAxis, 1, nTicks, tickType, ylab, dd);/* Figure out which Z axis to draw */if (lowest(v0[0]/v0[3], v1[0]/v1[3], v2[0]/v2[3], v3[0]/v3[3])) {zAxis = 4;} else if (lowest(v1[0]/v1[3], v0[0]/v0[3], v2[0]/v2[3], v3[0]/v3[3])) {zAxis = 5;} else if (lowest(v2[0]/v2[3], v1[0]/v1[3], v0[0]/v0[3], v3[0]/v3[3])) {zAxis = 6;} else if (lowest(v3[0]/v3[3], v1[0]/v1[3], v2[0]/v2[3], v0[0]/v0[3])) {zAxis = 7;} elsewarning("Axes orientation not calculated");PerspAxis(x, y, z, zAxis, 2, nTicks, tickType, zlab, dd);dd->gp.xpd = xpdsave;}SEXP do_persp(SEXP call, SEXP op, SEXP args, SEXP env){SEXP x, y, z, xlim, ylim, zlim;SEXP depth, index, originalArgs;SEXP col, border, xlab, ylab, zlab;double theta, phi, r, d;double ltheta, lphi;double expand, xc, yc, zc, xs, ys, zs;int i, j, scale, ncol, dobox, doaxes, nTicks, tickType;DevDesc *dd;if (length(args) < 18)errorcall(call, "too few parameters");gcall = call;originalArgs = args;PROTECT(x = coerceVector(CAR(args), REALSXP));if (length(x) < 2) errorcall(call, "invalid x argument");args = CDR(args);PROTECT(y = coerceVector(CAR(args), REALSXP));if (length(y) < 2) errorcall(call, "invalid y argument");args = CDR(args);PROTECT(z = coerceVector(CAR(args), REALSXP));if (!isMatrix(z) || nrows(z) != length(x) || ncols(z) != length(y))errorcall(call, "invalid z argument");args = CDR(args);PROTECT(xlim = coerceVector(CAR(args), REALSXP));if (length(xlim) != 2) errorcall(call, "invalid xlim argument");args = CDR(args);PROTECT(ylim = coerceVector(CAR(args), REALSXP));if (length(ylim) != 2) errorcall(call, "invalid ylim argument");args = CDR(args);PROTECT(zlim = coerceVector(CAR(args), REALSXP));if (length(zlim) != 2) errorcall(call, "invalid zlim argument");args = CDR(args);/* Checks on x/y/z Limits */if (!LimitCheck(REAL(xlim), &xc, &xs))errorcall(call, "invalid x limits");if (!LimitCheck(REAL(ylim), &yc, &ys))errorcall(call, "invalid y limits");if (!LimitCheck(REAL(zlim), &zc, &zs))errorcall(call, "invalid z limits");theta = asReal(CAR(args)); args = CDR(args);phi = asReal(CAR(args)); args = CDR(args);r = asReal(CAR(args)); args = CDR(args);d = asReal(CAR(args)); args = CDR(args);scale = asLogical(CAR(args)); args = CDR(args);expand = asReal(CAR(args)); args = CDR(args);col = CAR(args); args = CDR(args);border = CAR(args); args = CDR(args);ltheta = asReal(CAR(args)); args = CDR(args);lphi = asReal(CAR(args)); args = CDR(args);Shade = asReal(CAR(args)); args = CDR(args);dobox = asLogical(CAR(args)); args = CDR(args);doaxes = asLogical(CAR(args)); args = CDR(args);nTicks = asInteger(CAR(args)); args = CDR(args);tickType = asInteger(CAR(args)); args = CDR(args);xlab = CAR(args); args = CDR(args);ylab = CAR(args); args = CDR(args);zlab = CAR(args); args = CDR(args);if (R_FINITE(Shade) && Shade <= 0) Shade = 1;if (R_FINITE(ltheta) && R_FINITE(lphi) && R_FINITE(Shade))DoLighting = 1;elseDoLighting = 0;if (!scale) {double s;s = xs;if (s < ys) s = ys;if (s < zs) s = zs;xs = s; ys = s; zs = s;}/* Parameter Checks */if (!R_FINITE(theta) || !R_FINITE(phi) || !R_FINITE(r) || !R_FINITE(d) ||d < 0 || r < 0)errorcall(call, "invalid viewing parameters");if (!R_FINITE(expand) || expand < 0)errorcall(call, "invalid expand value");if (scale == NA_LOGICAL)scale = 0;if ((nTicks == NA_INTEGER) || (nTicks < 0))errorcall(call, "invalid nticks value");if ((tickType == NA_INTEGER) || (tickType < 1) || (tickType > 2))errorcall(call, "invalid ticktype value");dd = GNewPlot(call != R_NilValue, NA_LOGICAL);PROTECT(col = FixupCol(col, dd->gp.bg));ncol = LENGTH(col);if (ncol < 1) errorcall(call, "invalid col specification");PROTECT(border = FixupCol(border, dd->gp.fg));if (length(border) < 1) errorcall(call, "invalid border specification");GSetState(1, dd);GSavePars(dd);RecordGraphicsCall(call);ProcessInlinePars(args, dd);if (length(border) > 1)dd->gp.fg = INTEGER(border)[0];dd->gp.xlog = 0;dd->gp.ylog = 0;/* Set up the light vector (if any) */if (DoLighting)SetUpLight(ltheta, lphi);/* Mark box edges as undrawn */for (i = 0; i< 12; i++)EdgeDone[i] = 0;/* Specify the viewing transformation. */SetToIdentity(VT); /* Initialization */Translate(-xc, -yc, -zc); /* center at the origin */Scale(1/xs, 1/ys, expand/zs); /* scale extents to [-1,1] */XRotate(-90.0); /* rotate x-y plane to horizontal */YRotate(-theta); /* azimuthal rotation */XRotate(phi); /* elevation rotation */Translate(0.0, 0.0, -r - d); /* translate the eyepoint to the origin */Perspective(d); /* perspective *//* Specify the plotting window. *//* Here we map the vertices of the cube *//* [xmin,xmax]*[ymin,ymax]*[zmin,zmax] *//* to the screen and then chose a window *//* which is symmetric about (0,0). */PerspWindow(REAL(xlim), REAL(ylim), REAL(zlim), dd);/* Compute facet order. */PROTECT(depth = allocVector(REALSXP, (nrows(z) - 1)*(ncols(z) - 1)));PROTECT(index = allocVector(INTSXP, (nrows(z) - 1)*(ncols(z) - 1)));DepthOrder(REAL(z), REAL(x), REAL(y), nrows(z), ncols(z),REAL(depth), INTEGER(index));/* Now we order the facets by depth *//* and then draw them back to front. *//* This is the "painters" algorithm. */GMode(1, dd);if (dobox) {PerspBox(0, REAL(xlim), REAL(ylim), REAL(zlim), dd);if (doaxes)PerspAxes(REAL(xlim), REAL(ylim), REAL(zlim),CHAR(STRING_ELT(xlab, 0)), CHAR(STRING_ELT(ylab, 0)),CHAR(STRING_ELT(zlab, 0)),nTicks, tickType, dd);}DrawFacets(REAL(z), REAL(x), REAL(y), nrows(z), ncols(z), INTEGER(index),1/xs, 1/ys, expand/zs,INTEGER(col), ncol, INTEGER(border)[0]);if (dobox)PerspBox(1, REAL(xlim), REAL(ylim), REAL(zlim), dd);GMode(0, dd);GRestorePars(dd);UNPROTECT(10);if (call != R_NilValue)recordGraphicOperation(op, originalArgs, dd);PROTECT(x = allocVector(REALSXP, 16));PROTECT(y = allocVector(INTSXP, 2));for (i = 0; i < 4; i++)for (j = 0; j < 4; j++) {REAL(x)[i + j * 4] = VT[i][j];}INTEGER(y)[0] = 4;INTEGER(y)[1] = 4;setAttrib(x, R_DimSymbol, y);UNPROTECT(2);return x;}