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Diffstat (limited to 'tk8.6/generic/tkTrig.c')
| -rw-r--r-- | tk8.6/generic/tkTrig.c | 1753 |
1 files changed, 0 insertions, 1753 deletions
diff --git a/tk8.6/generic/tkTrig.c b/tk8.6/generic/tkTrig.c deleted file mode 100644 index a2bf456..0000000 --- a/tk8.6/generic/tkTrig.c +++ /dev/null @@ -1,1753 +0,0 @@ -/* - * 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: - */ |