--- /dev/null
+/*
+ * tkTrig.c --
+ *
+ * This file contains a collection of trigonometry utility
+ * routines that are used by Tk and in particular by the
+ * canvas code. It also has miscellaneous geometry functions
+ * used by canvases.
+ *
+ * Copyright (c) 1992-1994 The Regents of the University of California.
+ * Copyright (c) 1994-1997 Sun Microsystems, Inc.
+ *
+ * See the file "license.terms" for information on usage and redistribution
+ * of this file, and for a DISCLAIMER OF ALL WARRANTIES.
+ *
+ * RCS: @(#) $Id$
+ */
+
+#include <stdio.h>
+#include "tkInt.h"
+#include "tkPort.h"
+#include "tkCanvas.h"
+
+#undef MIN
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#undef MAX
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#ifndef PI
+# define PI 3.14159265358979323846
+#endif /* PI */
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkLineToPoint --
+ *
+ * Compute the distance from a point to a finite line segment.
+ *
+ * Results:
+ * The return value is the distance from the line segment
+ * whose end-points are *end1Ptr and *end2Ptr to the point
+ * given by *pointPtr.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+double
+TkLineToPoint(end1Ptr, end2Ptr, pointPtr)
+ double end1Ptr[2]; /* Coordinates of first end-point of line. */
+ double end2Ptr[2]; /* Coordinates of second end-point of line. */
+ double pointPtr[2]; /* Points to coords for point. */
+{
+ double x, y;
+
+ /*
+ * Compute the point on the line that is closest to the
+ * point. This must be done separately for vertical edges,
+ * horizontal edges, and other edges.
+ */
+
+ if (end1Ptr[0] == end2Ptr[0]) {
+
+ /*
+ * Vertical edge.
+ */
+
+ x = end1Ptr[0];
+ if (end1Ptr[1] >= end2Ptr[1]) {
+ y = MIN(end1Ptr[1], pointPtr[1]);
+ y = MAX(y, end2Ptr[1]);
+ } else {
+ y = MIN(end2Ptr[1], pointPtr[1]);
+ y = MAX(y, end1Ptr[1]);
+ }
+ } else if (end1Ptr[1] == end2Ptr[1]) {
+
+ /*
+ * Horizontal edge.
+ */
+
+ y = end1Ptr[1];
+ if (end1Ptr[0] >= end2Ptr[0]) {
+ x = MIN(end1Ptr[0], pointPtr[0]);
+ x = MAX(x, end2Ptr[0]);
+ } else {
+ x = MIN(end2Ptr[0], pointPtr[0]);
+ x = MAX(x, end1Ptr[0]);
+ }
+ } else {
+ double m1, b1, m2, b2;
+
+ /*
+ * The edge is neither horizontal nor vertical. Convert the
+ * edge to a line equation of the form y = m1*x + b1. Then
+ * compute a line perpendicular to this edge but passing
+ * through the point, also in the form y = m2*x + b2.
+ */
+
+ m1 = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]);
+ b1 = end1Ptr[1] - m1*end1Ptr[0];
+ m2 = -1.0/m1;
+ b2 = pointPtr[1] - m2*pointPtr[0];
+ x = (b2 - b1)/(m1 - m2);
+ y = m1*x + b1;
+ if (end1Ptr[0] > end2Ptr[0]) {
+ if (x > end1Ptr[0]) {
+ x = end1Ptr[0];
+ y = end1Ptr[1];
+ } else if (x < end2Ptr[0]) {
+ x = end2Ptr[0];
+ y = end2Ptr[1];
+ }
+ } else {
+ if (x > end2Ptr[0]) {
+ x = end2Ptr[0];
+ y = end2Ptr[1];
+ } else if (x < end1Ptr[0]) {
+ x = end1Ptr[0];
+ y = end1Ptr[1];
+ }
+ }
+ }
+
+ /*
+ * Compute the distance to the closest point.
+ */
+
+ return hypot(pointPtr[0] - x, pointPtr[1] - y);
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkLineToArea --
+ *
+ * Determine whether a line lies entirely inside, entirely
+ * outside, or overlapping a given rectangular area.
+ *
+ * Results:
+ * -1 is returned if the line given by end1Ptr and end2Ptr
+ * is entirely outside the rectangle given by rectPtr. 0 is
+ * returned if the polygon overlaps the rectangle, and 1 is
+ * returned if the polygon is entirely inside the rectangle.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+int
+TkLineToArea(end1Ptr, end2Ptr, rectPtr)
+ double end1Ptr[2]; /* X and y coordinates for one endpoint
+ * of line. */
+ double end2Ptr[2]; /* X and y coordinates for other endpoint
+ * of line. */
+ double rectPtr[4]; /* Points to coords for rectangle, in the
+ * order x1, y1, x2, y2. X1 must be no
+ * larger than x2, and y1 no larger than y2. */
+{
+ int inside1, inside2;
+
+ /*
+ * First check the two points individually to see whether they
+ * are inside the rectangle or not.
+ */
+
+ inside1 = (end1Ptr[0] >= rectPtr[0]) && (end1Ptr[0] <= rectPtr[2])
+ && (end1Ptr[1] >= rectPtr[1]) && (end1Ptr[1] <= rectPtr[3]);
+ inside2 = (end2Ptr[0] >= rectPtr[0]) && (end2Ptr[0] <= rectPtr[2])
+ && (end2Ptr[1] >= rectPtr[1]) && (end2Ptr[1] <= rectPtr[3]);
+ if (inside1 != inside2) {
+ return 0;
+ }
+ if (inside1 & inside2) {
+ return 1;
+ }
+
+ /*
+ * Both points are outside the rectangle, but still need to check
+ * for intersections between the line and the rectangle. Horizontal
+ * and vertical lines are particularly easy, so handle them
+ * separately.
+ */
+
+ if (end1Ptr[0] == end2Ptr[0]) {
+ /*
+ * Vertical line.
+ */
+
+ if (((end1Ptr[1] >= rectPtr[1]) ^ (end2Ptr[1] >= rectPtr[1]))
+ && (end1Ptr[0] >= rectPtr[0])
+ && (end1Ptr[0] <= rectPtr[2])) {
+ return 0;
+ }
+ } else if (end1Ptr[1] == end2Ptr[1]) {
+ /*
+ * Horizontal line.
+ */
+
+ if (((end1Ptr[0] >= rectPtr[0]) ^ (end2Ptr[0] >= rectPtr[0]))
+ && (end1Ptr[1] >= rectPtr[1])
+ && (end1Ptr[1] <= rectPtr[3])) {
+ return 0;
+ }
+ } else {
+ double m, x, y, low, high;
+
+ /*
+ * Diagonal line. Compute slope of line and use
+ * for intersection checks against each of the
+ * sides of the rectangle: left, right, bottom, top.
+ */
+
+ m = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]);
+ if (end1Ptr[0] < end2Ptr[0]) {
+ low = end1Ptr[0]; high = end2Ptr[0];
+ } else {
+ low = end2Ptr[0]; high = end1Ptr[0];
+ }
+
+ /*
+ * Left edge.
+ */
+
+ y = end1Ptr[1] + (rectPtr[0] - end1Ptr[0])*m;
+ if ((rectPtr[0] >= low) && (rectPtr[0] <= high)
+ && (y >= rectPtr[1]) && (y <= rectPtr[3])) {
+ return 0;
+ }
+
+ /*
+ * Right edge.
+ */
+
+ y += (rectPtr[2] - rectPtr[0])*m;
+ if ((y >= rectPtr[1]) && (y <= rectPtr[3])
+ && (rectPtr[2] >= low) && (rectPtr[2] <= high)) {
+ return 0;
+ }
+
+ /*
+ * Bottom edge.
+ */
+
+ if (end1Ptr[1] < end2Ptr[1]) {
+ low = end1Ptr[1]; high = end2Ptr[1];
+ } else {
+ low = end2Ptr[1]; high = end1Ptr[1];
+ }
+ x = end1Ptr[0] + (rectPtr[1] - end1Ptr[1])/m;
+ if ((x >= rectPtr[0]) && (x <= rectPtr[2])
+ && (rectPtr[1] >= low) && (rectPtr[1] <= high)) {
+ return 0;
+ }
+
+ /*
+ * Top edge.
+ */
+
+ x += (rectPtr[3] - rectPtr[1])/m;
+ if ((x >= rectPtr[0]) && (x <= rectPtr[2])
+ && (rectPtr[3] >= low) && (rectPtr[3] <= high)) {
+ return 0;
+ }
+ }
+ return -1;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkThickPolyLineToArea --
+ *
+ * This procedure is called to determine whether a connected
+ * series of line segments lies entirely inside, entirely
+ * outside, or overlapping a given rectangular area.
+ *
+ * Results:
+ * -1 is returned if the lines are entirely outside the area,
+ * 0 if they overlap, and 1 if they are entirely inside the
+ * given area.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+ /* ARGSUSED */
+int
+TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr)
+ double *coordPtr; /* Points to an array of coordinates for
+ * the polyline: x0, y0, x1, y1, ... */
+ int numPoints; /* Total number of points at *coordPtr. */
+ double width; /* Width of each line segment. */
+ int capStyle; /* How are end-points of polyline drawn?
+ * CapRound, CapButt, or CapProjecting. */
+ int joinStyle; /* How are joints in polyline drawn?
+ * JoinMiter, JoinRound, or JoinBevel. */
+ double *rectPtr; /* Rectangular area to check against. */
+{
+ double radius, poly[10];
+ int count;
+ int changedMiterToBevel; /* Non-zero means that a mitered corner
+ * had to be treated as beveled after all
+ * because the angle was < 11 degrees. */
+ int inside; /* Tentative guess about what to return,
+ * based on all points seen so far: one
+ * means everything seen so far was
+ * inside the area; -1 means everything
+ * was outside the area. 0 means overlap
+ * has been found. */
+
+ radius = width/2.0;
+ inside = -1;
+
+ if ((coordPtr[0] >= rectPtr[0]) && (coordPtr[0] <= rectPtr[2])
+ && (coordPtr[1] >= rectPtr[1]) && (coordPtr[1] <= rectPtr[3])) {
+ inside = 1;
+ }
+
+ /*
+ * Iterate through all of the edges of the line, computing a polygon
+ * for each edge and testing the area against that polygon. In
+ * addition, there are additional tests to deal with rounded joints
+ * and caps.
+ */
+
+ changedMiterToBevel = 0;
+ for (count = numPoints; count >= 2; count--, coordPtr += 2) {
+
+ /*
+ * If rounding is done around the first point of the edge
+ * then test a circular region around the point with the
+ * area.
+ */
+
+ if (((capStyle == CapRound) && (count == numPoints))
+ || ((joinStyle == JoinRound) && (count != numPoints))) {
+ poly[0] = coordPtr[0] - radius;
+ poly[1] = coordPtr[1] - radius;
+ poly[2] = coordPtr[0] + radius;
+ poly[3] = coordPtr[1] + radius;
+ if (TkOvalToArea(poly, rectPtr) != inside) {
+ return 0;
+ }
+ }
+
+ /*
+ * Compute the polygonal shape corresponding to this edge,
+ * consisting of two points for the first point of the edge
+ * and two points for the last point of the edge.
+ */
+
+ if (count == numPoints) {
+ TkGetButtPoints(coordPtr+2, coordPtr, width,
+ capStyle == CapProjecting, poly, poly+2);
+ } else if ((joinStyle == JoinMiter) && !changedMiterToBevel) {
+ poly[0] = poly[6];
+ poly[1] = poly[7];
+ poly[2] = poly[4];
+ poly[3] = poly[5];
+ } else {
+ TkGetButtPoints(coordPtr+2, coordPtr, width, 0, poly, poly+2);
+
+ /*
+ * If the last joint was beveled, then also check a
+ * polygon comprising the last two points of the previous
+ * polygon and the first two from this polygon; this checks
+ * the wedges that fill the beveled joint.
+ */
+
+ if ((joinStyle == JoinBevel) || changedMiterToBevel) {
+ poly[8] = poly[0];
+ poly[9] = poly[1];
+ if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
+ return 0;
+ }
+ changedMiterToBevel = 0;
+ }
+ }
+ if (count == 2) {
+ TkGetButtPoints(coordPtr, coordPtr+2, width,
+ capStyle == CapProjecting, poly+4, poly+6);
+ } else if (joinStyle == JoinMiter) {
+ if (TkGetMiterPoints(coordPtr, coordPtr+2, coordPtr+4,
+ (double) width, poly+4, poly+6) == 0) {
+ changedMiterToBevel = 1;
+ TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4,
+ poly+6);
+ }
+ } else {
+ TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4, poly+6);
+ }
+ poly[8] = poly[0];
+ poly[9] = poly[1];
+ if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
+ return 0;
+ }
+ }
+
+ /*
+ * If caps are rounded, check the cap around the final point
+ * of the line.
+ */
+
+ if (capStyle == CapRound) {
+ poly[0] = coordPtr[0] - radius;
+ poly[1] = coordPtr[1] - radius;
+ poly[2] = coordPtr[0] + radius;
+ poly[3] = coordPtr[1] + radius;
+ if (TkOvalToArea(poly, rectPtr) != inside) {
+ return 0;
+ }
+ }
+
+ return inside;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkPolygonToPoint --
+ *
+ * Compute the distance from a point to a polygon.
+ *
+ * Results:
+ * The return value is 0.0 if the point referred to by
+ * pointPtr is within the polygon referred to by polyPtr
+ * and numPoints. Otherwise the return value is the
+ * distance of the point from the polygon.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+double
+TkPolygonToPoint(polyPtr, numPoints, pointPtr)
+ double *polyPtr; /* Points to an array coordinates for
+ * closed polygon: x0, y0, x1, y1, ...
+ * The polygon may be self-intersecting. */
+ int numPoints; /* Total number of points at *polyPtr. */
+ double *pointPtr; /* Points to coords for point. */
+{
+ double bestDist; /* Closest distance between point and
+ * any edge in polygon. */
+ int intersections; /* Number of edges in the polygon that
+ * intersect a ray extending vertically
+ * upwards from the point to infinity. */
+ int count;
+ register double *pPtr;
+
+ /*
+ * Iterate through all of the edges in the polygon, updating
+ * bestDist and intersections.
+ *
+ * TRICKY POINT: when computing intersections, include left
+ * x-coordinate of line within its range, but not y-coordinate.
+ * Otherwise if the point lies exactly below a vertex we'll
+ * count it as two intersections.
+ */
+
+ bestDist = 1.0e36;
+ intersections = 0;
+
+ for (count = numPoints, pPtr = polyPtr; count > 1; count--, pPtr += 2) {
+ double x, y, dist;
+
+ /*
+ * Compute the point on the current edge closest to the point
+ * and update the intersection count. This must be done
+ * separately for vertical edges, horizontal edges, and
+ * other edges.
+ */
+
+ if (pPtr[2] == pPtr[0]) {
+
+ /*
+ * Vertical edge.
+ */
+
+ x = pPtr[0];
+ if (pPtr[1] >= pPtr[3]) {
+ y = MIN(pPtr[1], pointPtr[1]);
+ y = MAX(y, pPtr[3]);
+ } else {
+ y = MIN(pPtr[3], pointPtr[1]);
+ y = MAX(y, pPtr[1]);
+ }
+ } else if (pPtr[3] == pPtr[1]) {
+
+ /*
+ * Horizontal edge.
+ */
+
+ y = pPtr[1];
+ if (pPtr[0] >= pPtr[2]) {
+ x = MIN(pPtr[0], pointPtr[0]);
+ x = MAX(x, pPtr[2]);
+ if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[0])
+ && (pointPtr[0] >= pPtr[2])) {
+ intersections++;
+ }
+ } else {
+ x = MIN(pPtr[2], pointPtr[0]);
+ x = MAX(x, pPtr[0]);
+ if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[2])
+ && (pointPtr[0] >= pPtr[0])) {
+ intersections++;
+ }
+ }
+ } else {
+ double m1, b1, m2, b2;
+ int lower; /* Non-zero means point below line. */
+
+ /*
+ * The edge is neither horizontal nor vertical. Convert the
+ * edge to a line equation of the form y = m1*x + b1. Then
+ * compute a line perpendicular to this edge but passing
+ * through the point, also in the form y = m2*x + b2.
+ */
+
+ m1 = (pPtr[3] - pPtr[1])/(pPtr[2] - pPtr[0]);
+ b1 = pPtr[1] - m1*pPtr[0];
+ m2 = -1.0/m1;
+ b2 = pointPtr[1] - m2*pointPtr[0];
+ x = (b2 - b1)/(m1 - m2);
+ y = m1*x + b1;
+ if (pPtr[0] > pPtr[2]) {
+ if (x > pPtr[0]) {
+ x = pPtr[0];
+ y = pPtr[1];
+ } else if (x < pPtr[2]) {
+ x = pPtr[2];
+ y = pPtr[3];
+ }
+ } else {
+ if (x > pPtr[2]) {
+ x = pPtr[2];
+ y = pPtr[3];
+ } else if (x < pPtr[0]) {
+ x = pPtr[0];
+ y = pPtr[1];
+ }
+ }
+ lower = (m1*pointPtr[0] + b1) > pointPtr[1];
+ if (lower && (pointPtr[0] >= MIN(pPtr[0], pPtr[2]))
+ && (pointPtr[0] < MAX(pPtr[0], pPtr[2]))) {
+ intersections++;
+ }
+ }
+
+ /*
+ * Compute the distance to the closest point, and see if that
+ * is the best distance seen so far.
+ */
+
+ dist = hypot(pointPtr[0] - x, pointPtr[1] - y);
+ if (dist < bestDist) {
+ bestDist = dist;
+ }
+ }
+
+ /*
+ * We've processed all of the points. If the number of intersections
+ * is odd, the point is inside the polygon.
+ */
+
+ if (intersections & 0x1) {
+ return 0.0;
+ }
+ return bestDist;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkPolygonToArea --
+ *
+ * Determine whether a polygon lies entirely inside, entirely
+ * outside, or overlapping a given rectangular area.
+ *
+ * Results:
+ * -1 is returned if the polygon given by polyPtr and numPoints
+ * is entirely outside the rectangle given by rectPtr. 0 is
+ * returned if the polygon overlaps the rectangle, and 1 is
+ * returned if the polygon is entirely inside the rectangle.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+int
+TkPolygonToArea(polyPtr, numPoints, rectPtr)
+ double *polyPtr; /* Points to an array coordinates for
+ * closed polygon: x0, y0, x1, y1, ...
+ * The polygon may be self-intersecting. */
+ int numPoints; /* Total number of points at *polyPtr. */
+ register double *rectPtr; /* Points to coords for rectangle, in the
+ * order x1, y1, x2, y2. X1 and y1 must
+ * be lower-left corner. */
+{
+ int state; /* State of all edges seen so far (-1 means
+ * outside, 1 means inside, won't ever be
+ * 0). */
+ int count;
+ register double *pPtr;
+
+ /*
+ * Iterate over all of the edges of the polygon and test them
+ * against the rectangle. Can quit as soon as the state becomes
+ * "intersecting".
+ */
+
+ state = TkLineToArea(polyPtr, polyPtr+2, rectPtr);
+ if (state == 0) {
+ return 0;
+ }
+ for (pPtr = polyPtr+2, count = numPoints-1; count >= 2;
+ pPtr += 2, count--) {
+ if (TkLineToArea(pPtr, pPtr+2, rectPtr) != state) {
+ return 0;
+ }
+ }
+
+ /*
+ * If all of the edges were inside the rectangle we're done.
+ * If all of the edges were outside, then the rectangle could
+ * still intersect the polygon (if it's entirely enclosed).
+ * Call TkPolygonToPoint to figure this out.
+ */
+
+ if (state == 1) {
+ return 1;
+ }
+ if (TkPolygonToPoint(polyPtr, numPoints, rectPtr) == 0.0) {
+ return 0;
+ }
+ return -1;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkOvalToPoint --
+ *
+ * Computes the distance from a given point to a given
+ * oval, in canvas units.
+ *
+ * Results:
+ * The return value is 0 if the point given by *pointPtr is
+ * inside the oval. If the point isn't inside the
+ * oval then the return value is approximately the distance
+ * from the point to the oval. If the oval is filled, then
+ * anywhere in the interior is considered "inside"; if
+ * the oval isn't filled, then "inside" means only the area
+ * occupied by the outline.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+ /* ARGSUSED */
+double
+TkOvalToPoint(ovalPtr, width, filled, pointPtr)
+ double ovalPtr[4]; /* Pointer to array of four coordinates
+ * (x1, y1, x2, y2) defining oval's bounding
+ * box. */
+ double width; /* Width of outline for oval. */
+ int filled; /* Non-zero means oval should be treated as
+ * filled; zero means only consider outline. */
+ double pointPtr[2]; /* Coordinates of point. */
+{
+ double xDelta, yDelta, scaledDistance, distToOutline, distToCenter;
+ double xDiam, yDiam;
+
+ /*
+ * Compute the distance between the center of the oval and the
+ * point in question, using a coordinate system where the oval
+ * has been transformed to a circle with unit radius.
+ */
+
+ xDelta = (pointPtr[0] - (ovalPtr[0] + ovalPtr[2])/2.0);
+ yDelta = (pointPtr[1] - (ovalPtr[1] + ovalPtr[3])/2.0);
+ distToCenter = hypot(xDelta, yDelta);
+ scaledDistance = hypot(xDelta / ((ovalPtr[2] + width - ovalPtr[0])/2.0),
+ yDelta / ((ovalPtr[3] + width - ovalPtr[1])/2.0));
+
+
+ /*
+ * If the scaled distance is greater than 1 then it means no
+ * hit. Compute the distance from the point to the edge of
+ * the circle, then scale this distance back to the original
+ * coordinate system.
+ *
+ * Note: this distance isn't completely accurate. It's only
+ * an approximation, and it can overestimate the correct
+ * distance when the oval is eccentric.
+ */
+
+ if (scaledDistance > 1.0) {
+ return (distToCenter/scaledDistance) * (scaledDistance - 1.0);
+ }
+
+ /*
+ * Scaled distance less than 1 means the point is inside the
+ * outer edge of the oval. If this is a filled oval, then we
+ * have a hit. Otherwise, do the same computation as above
+ * (scale back to original coordinate system), but also check
+ * to see if the point is within the width of the outline.
+ */
+
+ if (filled) {
+ return 0.0;
+ }
+ if (scaledDistance > 1E-10) {
+ distToOutline = (distToCenter/scaledDistance) * (1.0 - scaledDistance)
+ - width;
+ } else {
+ /*
+ * Avoid dividing by a very small number (it could cause an
+ * arithmetic overflow). This problem occurs if the point is
+ * very close to the center of the oval.
+ */
+
+ xDiam = ovalPtr[2] - ovalPtr[0];
+ yDiam = ovalPtr[3] - ovalPtr[1];
+ if (xDiam < yDiam) {
+ distToOutline = (xDiam - width)/2;
+ } else {
+ distToOutline = (yDiam - width)/2;
+ }
+ }
+
+ if (distToOutline < 0.0) {
+ return 0.0;
+ }
+ return distToOutline;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkOvalToArea --
+ *
+ * Determine whether an oval lies entirely inside, entirely
+ * outside, or overlapping a given rectangular area.
+ *
+ * Results:
+ * -1 is returned if the oval described by ovalPtr is entirely
+ * outside the rectangle given by rectPtr. 0 is returned if the
+ * oval overlaps the rectangle, and 1 is returned if the oval
+ * is entirely inside the rectangle.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+int
+TkOvalToArea(ovalPtr, rectPtr)
+ register double *ovalPtr; /* Points to coordinates definining the
+ * bounding rectangle for the oval: x1, y1,
+ * x2, y2. X1 must be less than x2 and y1
+ * less than y2. */
+ register double *rectPtr; /* Points to coords for rectangle, in the
+ * order x1, y1, x2, y2. X1 and y1 must
+ * be lower-left corner. */
+{
+ double centerX, centerY, radX, radY, deltaX, deltaY;
+
+ /*
+ * First, see if oval is entirely inside rectangle or entirely
+ * outside rectangle.
+ */
+
+ if ((rectPtr[0] <= ovalPtr[0]) && (rectPtr[2] >= ovalPtr[2])
+ && (rectPtr[1] <= ovalPtr[1]) && (rectPtr[3] >= ovalPtr[3])) {
+ return 1;
+ }
+ if ((rectPtr[2] < ovalPtr[0]) || (rectPtr[0] > ovalPtr[2])
+ || (rectPtr[3] < ovalPtr[1]) || (rectPtr[1] > ovalPtr[3])) {
+ return -1;
+ }
+
+ /*
+ * Next, go through the rectangle side by side. For each side
+ * of the rectangle, find the point on the side that is closest
+ * to the oval's center, and see if that point is inside the
+ * oval. If at least one such point is inside the oval, then
+ * the rectangle intersects the oval.
+ */
+
+ centerX = (ovalPtr[0] + ovalPtr[2])/2;
+ centerY = (ovalPtr[1] + ovalPtr[3])/2;
+ radX = (ovalPtr[2] - ovalPtr[0])/2;
+ radY = (ovalPtr[3] - ovalPtr[1])/2;
+
+ deltaY = rectPtr[1] - centerY;
+ if (deltaY < 0.0) {
+ deltaY = centerY - rectPtr[3];
+ if (deltaY < 0.0) {
+ deltaY = 0;
+ }
+ }
+ deltaY /= radY;
+ deltaY *= deltaY;
+
+ /*
+ * Left side:
+ */
+
+ deltaX = (rectPtr[0] - centerX)/radX;
+ deltaX *= deltaX;
+ if ((deltaX + deltaY) <= 1.0) {
+ return 0;
+ }
+
+ /*
+ * Right side:
+ */
+
+ deltaX = (rectPtr[2] - centerX)/radX;
+ deltaX *= deltaX;
+ if ((deltaX + deltaY) <= 1.0) {
+ return 0;
+ }
+
+ deltaX = rectPtr[0] - centerX;
+ if (deltaX < 0.0) {
+ deltaX = centerX - rectPtr[2];
+ if (deltaX < 0.0) {
+ deltaX = 0;
+ }
+ }
+ deltaX /= radX;
+ deltaX *= deltaX;
+
+ /*
+ * Bottom side:
+ */
+
+ deltaY = (rectPtr[1] - centerY)/radY;
+ deltaY *= deltaY;
+ if ((deltaX + deltaY) < 1.0) {
+ return 0;
+ }
+
+ /*
+ * Top side:
+ */
+
+ deltaY = (rectPtr[3] - centerY)/radY;
+ deltaY *= deltaY;
+ if ((deltaX + deltaY) < 1.0) {
+ return 0;
+ }
+
+ return -1;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkIncludePoint --
+ *
+ * Given a point and a generic canvas item header, expand
+ * the item's bounding box if needed to include the point.
+ *
+ * Results:
+ * None.
+ *
+ * Side effects:
+ * The boudn.
+ *
+ *--------------------------------------------------------------
+ */
+
+ /* ARGSUSED */
+void
+TkIncludePoint(itemPtr, pointPtr)
+ register Tk_Item *itemPtr; /* Item whose bounding box is
+ * being calculated. */
+ double *pointPtr; /* Address of two doubles giving
+ * x and y coordinates of point. */
+{
+ int tmp;
+
+ tmp = (int) (pointPtr[0] + 0.5);
+ if (tmp < itemPtr->x1) {
+ itemPtr->x1 = tmp;
+ }
+ if (tmp > itemPtr->x2) {
+ itemPtr->x2 = tmp;
+ }
+ tmp = (int) (pointPtr[1] + 0.5);
+ if (tmp < itemPtr->y1) {
+ itemPtr->y1 = tmp;
+ }
+ if (tmp > itemPtr->y2) {
+ itemPtr->y2 = tmp;
+ }
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkBezierScreenPoints --
+ *
+ * Given four control points, create a larger set of XPoints
+ * for a Bezier spline based on the points.
+ *
+ * Results:
+ * The array at *xPointPtr gets filled in with numSteps XPoints
+ * corresponding to the Bezier spline defined by the four
+ * control points. Note: no output point is generated for the
+ * first input point, but an output point *is* generated for
+ * the last input point.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+void
+TkBezierScreenPoints(canvas, control, numSteps, xPointPtr)
+ Tk_Canvas canvas; /* Canvas in which curve is to be
+ * drawn. */
+ double control[]; /* Array of coordinates for four
+ * control points: x0, y0, x1, y1,
+ * ... x3 y3. */
+ int numSteps; /* Number of curve points to
+ * generate. */
+ register XPoint *xPointPtr; /* Where to put new points. */
+{
+ int i;
+ double u, u2, u3, t, t2, t3;
+
+ for (i = 1; i <= numSteps; i++, xPointPtr++) {
+ t = ((double) i)/((double) numSteps);
+ t2 = t*t;
+ t3 = t2*t;
+ u = 1.0 - t;
+ u2 = u*u;
+ u3 = u2*u;
+ Tk_CanvasDrawableCoords(canvas,
+ (control[0]*u3 + 3.0 * (control[2]*t*u2 + control[4]*t2*u)
+ + control[6]*t3),
+ (control[1]*u3 + 3.0 * (control[3]*t*u2 + control[5]*t2*u)
+ + control[7]*t3),
+ &xPointPtr->x, &xPointPtr->y);
+ }
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkBezierPoints --
+ *
+ * Given four control points, create a larger set of points
+ * for a Bezier spline based on the points.
+ *
+ * Results:
+ * The array at *coordPtr gets filled in with 2*numSteps
+ * coordinates, which correspond to the Bezier spline defined
+ * by the four control points. Note: no output point is
+ * generated for the first input point, but an output point
+ * *is* generated for the last input point.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+void
+TkBezierPoints(control, numSteps, coordPtr)
+ double control[]; /* Array of coordinates for four
+ * control points: x0, y0, x1, y1,
+ * ... x3 y3. */
+ int numSteps; /* Number of curve points to
+ * generate. */
+ register double *coordPtr; /* Where to put new points. */
+{
+ int i;
+ double u, u2, u3, t, t2, t3;
+
+ for (i = 1; i <= numSteps; i++, coordPtr += 2) {
+ t = ((double) i)/((double) numSteps);
+ t2 = t*t;
+ t3 = t2*t;
+ u = 1.0 - t;
+ u2 = u*u;
+ u3 = u2*u;
+ coordPtr[0] = control[0]*u3
+ + 3.0 * (control[2]*t*u2 + control[4]*t2*u) + control[6]*t3;
+ coordPtr[1] = control[1]*u3
+ + 3.0 * (control[3]*t*u2 + control[5]*t2*u) + control[7]*t3;
+ }
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkMakeBezierCurve --
+ *
+ * Given a set of points, create a new set of points that fit
+ * parabolic splines to the line segments connecting the original
+ * points. Produces output points in either of two forms.
+ *
+ * Note: in spite of this procedure's name, it does *not* generate
+ * Bezier curves. Since only three control points are used for
+ * each curve segment, not four, the curves are actually just
+ * parabolic.
+ *
+ * Results:
+ * Either or both of the xPoints or dblPoints arrays are filled
+ * in. The return value is the number of points placed in the
+ * arrays. Note: if the first and last points are the same, then
+ * a closed curve is generated.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+int
+TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints)
+ Tk_Canvas canvas; /* Canvas in which curve is to be
+ * drawn. */
+ double *pointPtr; /* Array of input coordinates: x0,
+ * y0, x1, y1, etc.. */
+ int numPoints; /* Number of points at pointPtr. */
+ int numSteps; /* Number of steps to use for each
+ * spline segments (determines
+ * smoothness of curve). */
+ XPoint xPoints[]; /* Array of XPoints to fill in (e.g.
+ * for display. NULL means don't
+ * fill in any XPoints. */
+ double dblPoints[]; /* Array of points to fill in as
+ * doubles, in the form x0, y0,
+ * x1, y1, .... NULL means don't
+ * fill in anything in this form.
+ * Caller must make sure that this
+ * array has enough space. */
+{
+ int closed, outputPoints, i;
+ int numCoords = numPoints*2;
+ double control[8];
+
+ /*
+ * If the curve is a closed one then generate a special spline
+ * that spans the last points and the first ones. Otherwise
+ * just put the first point into the output.
+ */
+
+ if (!pointPtr) {
+ /* Of pointPtr == NULL, this function returns an upper limit.
+ * of the array size to store the coordinates. This can be
+ * used to allocate storage, before the actual coordinates
+ * are calculated. */
+ return 1 + numPoints * numSteps;
+ }
+
+ outputPoints = 0;
+ if ((pointPtr[0] == pointPtr[numCoords-2])
+ && (pointPtr[1] == pointPtr[numCoords-1])) {
+ closed = 1;
+ control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
+ control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
+ control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
+ control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
+ control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
+ control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
+ control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
+ control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
+ if (xPoints != NULL) {
+ Tk_CanvasDrawableCoords(canvas, control[0], control[1],
+ &xPoints->x, &xPoints->y);
+ TkBezierScreenPoints(canvas, control, numSteps, xPoints+1);
+ xPoints += numSteps+1;
+ }
+ if (dblPoints != NULL) {
+ dblPoints[0] = control[0];
+ dblPoints[1] = control[1];
+ TkBezierPoints(control, numSteps, dblPoints+2);
+ dblPoints += 2*(numSteps+1);
+ }
+ outputPoints += numSteps+1;
+ } else {
+ closed = 0;
+ if (xPoints != NULL) {
+ Tk_CanvasDrawableCoords(canvas, pointPtr[0], pointPtr[1],
+ &xPoints->x, &xPoints->y);
+ xPoints += 1;
+ }
+ if (dblPoints != NULL) {
+ dblPoints[0] = pointPtr[0];
+ dblPoints[1] = pointPtr[1];
+ dblPoints += 2;
+ }
+ outputPoints += 1;
+ }
+
+ for (i = 2; i < numPoints; i++, pointPtr += 2) {
+ /*
+ * Set up the first two control points. This is done
+ * differently for the first spline of an open curve
+ * than for other cases.
+ */
+
+ if ((i == 2) && !closed) {
+ control[0] = pointPtr[0];
+ control[1] = pointPtr[1];
+ control[2] = 0.333*pointPtr[0] + 0.667*pointPtr[2];
+ control[3] = 0.333*pointPtr[1] + 0.667*pointPtr[3];
+ } else {
+ control[0] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
+ control[1] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
+ control[2] = 0.167*pointPtr[0] + 0.833*pointPtr[2];
+ control[3] = 0.167*pointPtr[1] + 0.833*pointPtr[3];
+ }
+
+ /*
+ * Set up the last two control points. This is done
+ * differently for the last spline of an open curve
+ * than for other cases.
+ */
+
+ if ((i == (numPoints-1)) && !closed) {
+ control[4] = .667*pointPtr[2] + .333*pointPtr[4];
+ control[5] = .667*pointPtr[3] + .333*pointPtr[5];
+ control[6] = pointPtr[4];
+ control[7] = pointPtr[5];
+ } else {
+ control[4] = .833*pointPtr[2] + .167*pointPtr[4];
+ control[5] = .833*pointPtr[3] + .167*pointPtr[5];
+ control[6] = 0.5*pointPtr[2] + 0.5*pointPtr[4];
+ control[7] = 0.5*pointPtr[3] + 0.5*pointPtr[5];
+ }
+
+ /*
+ * If the first two points coincide, or if the last
+ * two points coincide, then generate a single
+ * straight-line segment by outputting the last control
+ * point.
+ */
+
+ if (((pointPtr[0] == pointPtr[2]) && (pointPtr[1] == pointPtr[3]))
+ || ((pointPtr[2] == pointPtr[4])
+ && (pointPtr[3] == pointPtr[5]))) {
+ if (xPoints != NULL) {
+ Tk_CanvasDrawableCoords(canvas, control[6], control[7],
+ &xPoints[0].x, &xPoints[0].y);
+ xPoints++;
+ }
+ if (dblPoints != NULL) {
+ dblPoints[0] = control[6];
+ dblPoints[1] = control[7];
+ dblPoints += 2;
+ }
+ outputPoints += 1;
+ continue;
+ }
+
+ /*
+ * Generate a Bezier spline using the control points.
+ */
+
+
+ if (xPoints != NULL) {
+ TkBezierScreenPoints(canvas, control, numSteps, xPoints);
+ xPoints += numSteps;
+ }
+ if (dblPoints != NULL) {
+ TkBezierPoints(control, numSteps, dblPoints);
+ dblPoints += 2*numSteps;
+ }
+ outputPoints += numSteps;
+ }
+ return outputPoints;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkMakeBezierPostscript --
+ *
+ * This procedure generates Postscript commands that create
+ * a path corresponding to a given Bezier curve.
+ *
+ * Results:
+ * None. Postscript commands to generate the path are appended
+ * to the interp's result.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+void
+TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints)
+ Tcl_Interp *interp; /* Interpreter in whose result the
+ * Postscript is to be stored. */
+ Tk_Canvas canvas; /* Canvas widget for which the
+ * Postscript is being generated. */
+ double *pointPtr; /* Array of input coordinates: x0,
+ * y0, x1, y1, etc.. */
+ int numPoints; /* Number of points at pointPtr. */
+{
+ int closed, i;
+ int numCoords = numPoints*2;
+ double control[8];
+ char buffer[200];
+
+ /*
+ * If the curve is a closed one then generate a special spline
+ * that spans the last points and the first ones. Otherwise
+ * just put the first point into the path.
+ */
+
+ if ((pointPtr[0] == pointPtr[numCoords-2])
+ && (pointPtr[1] == pointPtr[numCoords-1])) {
+ closed = 1;
+ control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
+ control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
+ control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
+ control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
+ control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
+ control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
+ control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
+ control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
+ sprintf(buffer, "%.15g %.15g moveto\n%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
+ control[0], Tk_CanvasPsY(canvas, control[1]),
+ control[2], Tk_CanvasPsY(canvas, control[3]),
+ control[4], Tk_CanvasPsY(canvas, control[5]),
+ control[6], Tk_CanvasPsY(canvas, control[7]));
+ } else {
+ closed = 0;
+ control[6] = pointPtr[0];
+ control[7] = pointPtr[1];
+ sprintf(buffer, "%.15g %.15g moveto\n",
+ control[6], Tk_CanvasPsY(canvas, control[7]));
+ }
+ Tcl_AppendResult(interp, buffer, (char *) NULL);
+
+ /*
+ * Cycle through all the remaining points in the curve, generating
+ * a curve section for each vertex in the linear path.
+ */
+
+ for (i = numPoints-2, pointPtr += 2; i > 0; i--, pointPtr += 2) {
+ control[2] = 0.333*control[6] + 0.667*pointPtr[0];
+ control[3] = 0.333*control[7] + 0.667*pointPtr[1];
+
+ /*
+ * Set up the last two control points. This is done
+ * differently for the last spline of an open curve
+ * than for other cases.
+ */
+
+ if ((i == 1) && !closed) {
+ control[6] = pointPtr[2];
+ control[7] = pointPtr[3];
+ } else {
+ control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
+ control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
+ }
+ control[4] = 0.333*control[6] + 0.667*pointPtr[0];
+ control[5] = 0.333*control[7] + 0.667*pointPtr[1];
+
+ sprintf(buffer, "%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
+ control[2], Tk_CanvasPsY(canvas, control[3]),
+ control[4], Tk_CanvasPsY(canvas, control[5]),
+ control[6], Tk_CanvasPsY(canvas, control[7]));
+ Tcl_AppendResult(interp, buffer, (char *) NULL);
+ }
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkGetMiterPoints --
+ *
+ * Given three points forming an angle, compute the
+ * coordinates of the inside and outside points of
+ * the mitered corner formed by a line of a given
+ * width at that angle.
+ *
+ * Results:
+ * If the angle formed by the three points is less than
+ * 11 degrees then 0 is returned and m1 and m2 aren't
+ * modified. Otherwise 1 is returned and the points at
+ * m1 and m2 are filled in with the positions of the points
+ * of the mitered corner.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+int
+TkGetMiterPoints(p1, p2, p3, width, m1, m2)
+ double p1[]; /* Points to x- and y-coordinates of point
+ * before vertex. */
+ double p2[]; /* Points to x- and y-coordinates of vertex
+ * for mitered joint. */
+ double p3[]; /* Points to x- and y-coordinates of point
+ * after vertex. */
+ double width; /* Width of line. */
+ double m1[]; /* Points to place to put "left" vertex
+ * point (see as you face from p1 to p2). */
+ double m2[]; /* Points to place to put "right" vertex
+ * point. */
+{
+ double theta1; /* Angle of segment p2-p1. */
+ double theta2; /* Angle of segment p2-p3. */
+ double theta; /* Angle between line segments (angle
+ * of joint). */
+ double theta3; /* Angle that bisects theta1 and
+ * theta2 and points to m1. */
+ double dist; /* Distance of miter points from p2. */
+ double deltaX, deltaY; /* X and y offsets cooresponding to
+ * dist (fudge factors for bounding
+ * box). */
+ double p1x, p1y, p2x, p2y, p3x, p3y;
+ static double elevenDegrees = (11.0*2.0*PI)/360.0;
+
+ /*
+ * Round the coordinates to integers to mimic what happens when the
+ * line segments are displayed; without this code, the bounding box
+ * of a mitered line can be miscomputed greatly.
+ */
+
+ p1x = floor(p1[0]+0.5);
+ p1y = floor(p1[1]+0.5);
+ p2x = floor(p2[0]+0.5);
+ p2y = floor(p2[1]+0.5);
+ p3x = floor(p3[0]+0.5);
+ p3y = floor(p3[1]+0.5);
+
+ if (p2y == p1y) {
+ theta1 = (p2x < p1x) ? 0 : PI;
+ } else if (p2x == p1x) {
+ theta1 = (p2y < p1y) ? PI/2.0 : -PI/2.0;
+ } else {
+ theta1 = atan2(p1y - p2y, p1x - p2x);
+ }
+ if (p3y == p2y) {
+ theta2 = (p3x > p2x) ? 0 : PI;
+ } else if (p3x == p2x) {
+ theta2 = (p3y > p2y) ? PI/2.0 : -PI/2.0;
+ } else {
+ theta2 = atan2(p3y - p2y, p3x - p2x);
+ }
+ theta = theta1 - theta2;
+ if (theta > PI) {
+ theta -= 2*PI;
+ } else if (theta < -PI) {
+ theta += 2*PI;
+ }
+ if ((theta < elevenDegrees) && (theta > -elevenDegrees)) {
+ return 0;
+ }
+ dist = 0.5*width/sin(0.5*theta);
+ if (dist < 0.0) {
+ dist = -dist;
+ }
+
+ /*
+ * Compute theta3 (make sure that it points to the left when
+ * looking from p1 to p2).
+ */
+
+ theta3 = (theta1 + theta2)/2.0;
+ if (sin(theta3 - (theta1 + PI)) < 0.0) {
+ theta3 += PI;
+ }
+ deltaX = dist*cos(theta3);
+ m1[0] = p2x + deltaX;
+ m2[0] = p2x - deltaX;
+ deltaY = dist*sin(theta3);
+ m1[1] = p2y + deltaY;
+ m2[1] = p2y - deltaY;
+ return 1;
+}
+\f
+/*
+ *--------------------------------------------------------------
+ *
+ * TkGetButtPoints --
+ *
+ * Given two points forming a line segment, compute the
+ * coordinates of two endpoints of a rectangle formed by
+ * bloating the line segment until it is width units wide.
+ *
+ * Results:
+ * There is no return value. M1 and m2 are filled in to
+ * correspond to m1 and m2 in the diagram below:
+ *
+ * ----------------* m1
+ * |
+ * p1 *---------------* p2
+ * |
+ * ----------------* m2
+ *
+ * M1 and m2 will be W units apart, with p2 centered between
+ * them and m1-m2 perpendicular to p1-p2. However, if
+ * "project" is true then m1 and m2 will be as follows:
+ *
+ * -------------------* m1
+ * p2 |
+ * p1 *---------------* |
+ * |
+ * -------------------* m2
+ *
+ * In this case p2 will be width/2 units from the segment m1-m2.
+ *
+ * Side effects:
+ * None.
+ *
+ *--------------------------------------------------------------
+ */
+
+void
+TkGetButtPoints(p1, p2, width, project, m1, m2)
+ double p1[]; /* Points to x- and y-coordinates of point
+ * before vertex. */
+ double p2[]; /* Points to x- and y-coordinates of vertex
+ * for mitered joint. */
+ double width; /* Width of line. */
+ int project; /* Non-zero means project p2 by an additional
+ * width/2 before computing m1 and m2. */
+ double m1[]; /* Points to place to put "left" result
+ * point, as you face from p1 to p2. */
+ double m2[]; /* Points to place to put "right" result
+ * point. */
+{
+ double length; /* Length of p1-p2 segment. */
+ double deltaX, deltaY; /* Increments in coords. */
+
+ width *= 0.5;
+ length = hypot(p2[0] - p1[0], p2[1] - p1[1]);
+ if (length == 0.0) {
+ m1[0] = m2[0] = p2[0];
+ m1[1] = m2[1] = p2[1];
+ } else {
+ deltaX = -width * (p2[1] - p1[1]) / length;
+ deltaY = width * (p2[0] - p1[0]) / length;
+ m1[0] = p2[0] + deltaX;
+ m2[0] = p2[0] - deltaX;
+ m1[1] = p2[1] + deltaY;
+ m2[1] = p2[1] - deltaY;
+ if (project) {
+ m1[0] += deltaY;
+ m2[0] += deltaY;
+ m1[1] -= deltaX;
+ m2[1] -= deltaX;
+ }
+ }
+}
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