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Diffstat (limited to 'tk8.6/generic/tkTrig.c')
| -rw-r--r-- | tk8.6/generic/tkTrig.c | 1753 |
1 files changed, 1753 insertions, 0 deletions
diff --git a/tk8.6/generic/tkTrig.c b/tk8.6/generic/tkTrig.c new file mode 100644 index 0000000..a2bf456 --- /dev/null +++ b/tk8.6/generic/tkTrig.c @@ -0,0 +1,1753 @@ +/* + * 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. + */ + +#include "tkInt.h" +#include "tkCanvas.h" + +#undef MIN +#define MIN(a,b) (((a) < (b)) ? (a) : (b)) +#undef MAX +#define MAX(a,b) (((a) > (b)) ? (a) : (b)) + +/* + *-------------------------------------------------------------- + * + * 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( + 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); +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; +} + +/* + *-------------------------------------------------------------- + * + * TkThickPolyLineToArea -- + * + * This function 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( + 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; +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; +} + +/* + *-------------------------------------------------------------- + * + * 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( + register double *ovalPtr, /* Points to coordinates defining 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; +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; + } +} + +/* + *-------------------------------------------------------------- + * + * TkBezierScreenPoints -- + * + * Given four control points, create a larger set of XPoints for a Bezier + * curve 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( + 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); + } +} + +/* + *-------------------------------------------------------------- + * + * TkBezierPoints -- + * + * Given four control points, create a larger set of points for a Bezier + * curve 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( + 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; + } +} + +/* + *-------------------------------------------------------------- + * + * 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: the name of this function should *not* be taken to mean that it + * interprets the input points as directly defining Bezier curves. + * Rather, it internally computes a Bezier curve representation of each + * parabolic spline segment. (These Bezier curves are then flattened to + * produce the points filled into the output arrays.) + * + * 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( + 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; +} + +/* + *-------------------------------------------------------------- + * + * TkMakeRawCurve -- + * + * Interpret the given set of points as the raw knots and control points + * defining a sequence of cubic Bezier curves. Create a new set of points + * that fit these Bezier curves. Output points are produced in either of + * two forms. + * + * 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. + * + * Side effects: + * None. + * + *-------------------------------------------------------------- + */ + +int +TkMakeRawCurve( + 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 curve + * segment (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 outputPoints, i; + int numSegments = (numPoints+1)/3; + double *segPtr; + + /* + * The input describes a curve with s Bezier curve segments if there are + * 3s+1, 3s, or 3s-1 input points. In the last two cases, 1 or 2 initial + * points from the first curve segment are reused as defining points also + * for the last curve segment. In the case of 3s input points, this will + * automatically close the curve. + */ + + if (!pointPtr) { + /* + * If 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 + numSegments * numSteps; + } + + outputPoints = 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; + + /* + * The next loop handles all curve segments except one that overlaps the + * end of the list of coordinates. + */ + + for (i=numPoints,segPtr=pointPtr ; i>=4 ; i-=3,segPtr+=6) { + if (segPtr[0]==segPtr[2] && segPtr[1]==segPtr[3] && + segPtr[4]==segPtr[6] && segPtr[5]==segPtr[7]) { + /* + * The control points on this segment are equal to their + * neighbouring knots, so this segment is just a straight line. A + * single point is sufficient. + */ + + if (xPoints != NULL) { + Tk_CanvasDrawableCoords(canvas, segPtr[6], segPtr[7], + &xPoints->x, &xPoints->y); + xPoints += 1; + } + if (dblPoints != NULL) { + dblPoints[0] = segPtr[6]; + dblPoints[1] = segPtr[7]; + dblPoints += 2; + } + outputPoints += 1; + } else { + /* + * This is a generic Bezier curve segment. + */ + + if (xPoints != NULL) { + TkBezierScreenPoints(canvas, segPtr, numSteps, xPoints); + xPoints += numSteps; + } + if (dblPoints != NULL) { + TkBezierPoints(segPtr, numSteps, dblPoints); + dblPoints += 2*numSteps; + } + outputPoints += numSteps; + } + } + + /* + * If at this point i>1, then there is some point which has not yet been + * used. Make another curve segment. + */ + + if (i > 1) { + int j; + double control[8]; + + /* + * Copy the relevant coordinates to control[], so that it can be + * passed as a unit to e.g. TkBezierPoints. + */ + + for (j=0; j<2*i; j++) { + control[j] = segPtr[j]; + } + for (; j<8; j++) { + control[j] = pointPtr[j-2*i]; + } + + /* + * Then we just do the same things as above. + */ + + if (control[0]==control[2] && control[1]==control[3] && + control[4]==control[6] && control[5]==control[7]) { + /* + * The control points on this segment are equal to their + * neighbouring knots, so this segment is just a straight line. A + * single point is sufficient. + */ + + if (xPoints != NULL) { + Tk_CanvasDrawableCoords(canvas, control[6], control[7], + &xPoints->x, &xPoints->y); + xPoints += 1; + } + if (dblPoints != NULL) { + dblPoints[0] = control[6]; + dblPoints[1] = control[7]; + dblPoints += 2; + } + outputPoints += 1; + } else { + /* + * This is a generic Bezier curve segment. + */ + + if (xPoints != NULL) { + TkBezierScreenPoints(canvas, control, numSteps, xPoints); + xPoints += numSteps; + } + if (dblPoints != NULL) { + TkBezierPoints(control, numSteps, dblPoints); + dblPoints += 2*numSteps; + } + outputPoints += numSteps; + } + } + + return outputPoints; +} + +/* + *-------------------------------------------------------------- + * + * TkMakeBezierPostscript -- + * + * This function 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( + 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]; + Tcl_Obj *psObj; + + /* + * 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]; + psObj = Tcl_ObjPrintf( + "%.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]; + psObj = Tcl_ObjPrintf("%.15g %.15g moveto\n", + control[6], Tk_CanvasPsY(canvas, control[7])); + } + + /* + * 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]; + + Tcl_AppendPrintfToObj(psObj, + "%.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_AppendObjToObj(Tcl_GetObjResult(interp), psObj); + Tcl_DecrRefCount(psObj); +} + +/* + *-------------------------------------------------------------- + * + * TkMakeRawCurvePostscript -- + * + * This function interprets the input points as the raw knot and control + * points for a curve composed of Bezier curve segments, just like + * TkMakeRawCurve. It generates Postscript commands that create a path + * corresponding to this given curve. + * + * Results: + * None. Postscript commands to generate the path are appended to the + * interp's result. + * + * Side effects: + * None. + * + *-------------------------------------------------------------- + */ + +void +TkMakeRawCurvePostscript( + 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 i; + double *segPtr; + Tcl_Obj *psObj; + + /* + * Put the first point into the path. + */ + + psObj = Tcl_ObjPrintf("%.15g %.15g moveto\n", + pointPtr[0], Tk_CanvasPsY(canvas, pointPtr[1])); + + /* + * Loop through all the remaining points in the curve, generating a + * straight line or curve section for every three of them. + */ + + for (i=numPoints-1,segPtr=pointPtr ; i>=3 ; i-=3,segPtr+=6) { + if (segPtr[0]==segPtr[2] && segPtr[1]==segPtr[3] && + segPtr[4]==segPtr[6] && segPtr[5]==segPtr[7]) { + /* + * The control points on this segment are equal to their + * neighbouring knots, so this segment is just a straight line. + */ + + Tcl_AppendPrintfToObj(psObj, "%.15g %.15g lineto\n", + segPtr[6], Tk_CanvasPsY(canvas, segPtr[7])); + } else { + /* + * This is a generic Bezier curve segment. + */ + + Tcl_AppendPrintfToObj(psObj, + "%.15g %.15g %.15g %.15g %.15g %.15g curveto\n", + segPtr[2], Tk_CanvasPsY(canvas, segPtr[3]), + segPtr[4], Tk_CanvasPsY(canvas, segPtr[5]), + segPtr[6], Tk_CanvasPsY(canvas, segPtr[7])); + } + } + + /* + * If there are any points left that haven't been used, then build the + * last segment and generate Postscript in the same way for that. + */ + + if (i > 0) { + int j; + double control[8]; + + for (j=0; j<2*i+2; j++) { + control[j] = segPtr[j]; + } + for (; j<8; j++) { + control[j] = pointPtr[j-2*i-2]; + } + + if (control[0]==control[2] && control[1]==control[3] && + control[4]==control[6] && control[5]==control[7]) { + /* + * Straight line. + */ + + Tcl_AppendPrintfToObj(psObj, "%.15g %.15g lineto\n", + control[6], Tk_CanvasPsY(canvas, control[7])); + } else { + /* + * Bezier curve segment. + */ + + Tcl_AppendPrintfToObj(psObj, + "%.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_AppendObjToObj(Tcl_GetObjResult(interp), psObj); + Tcl_DecrRefCount(psObj); +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; +#ifndef _MSC_VER + static const double elevenDegrees = (11.0*2.0*PI)/360.0; +#else /* msvc8 with -fp:strict requires it this way */ + static const double elevenDegrees = 0.19198621771937624; +#endif + + /* + * 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; +} + +/* + *-------------------------------------------------------------- + * + * 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( + 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; + } + } +} + +/* + * Local Variables: + * mode: c + * c-basic-offset: 4 + * fill-column: 78 + * End: + */ |