diff options
Diffstat (limited to 'generic/tkTrig.c')
| -rw-r--r-- | generic/tkTrig.c | 992 |
1 files changed, 635 insertions, 357 deletions
diff --git a/generic/tkTrig.c b/generic/tkTrig.c index 1e90cf3..d7439b3 100644 --- a/generic/tkTrig.c +++ b/generic/tkTrig.c @@ -1,21 +1,19 @@ -/* +/* * 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. + * 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. + * See the file "license.terms" for information on usage and redistribution of + * this file, and for a DISCLAIMER OF ALL WARRANTIES. */ #include <stdio.h> #include "tkInt.h" -#include "tkPort.h" #include "tkCanvas.h" #undef MIN @@ -34,9 +32,8 @@ * 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. + * 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. @@ -45,17 +42,17 @@ */ double -TkLineToPoint(end1Ptr, end2Ptr, pointPtr) - double end1Ptr[2]; /* Coordinates of first end-point of line. */ - double end2Ptr[2]; /* Coordinates of second end-point of line. */ - double pointPtr[2]; /* Points to coords for point. */ +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. + * 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]) { @@ -90,10 +87,10 @@ TkLineToPoint(end1Ptr, end2Ptr, pointPtr) 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. + * 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]); @@ -133,14 +130,14 @@ TkLineToPoint(end1Ptr, end2Ptr, pointPtr) * * TkLineToArea -- * - * Determine whether a line lies entirely inside, entirely - * outside, or overlapping a given rectangular area. + * 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. + * -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. @@ -149,20 +146,20 @@ TkLineToPoint(end1Ptr, end2Ptr, pointPtr) */ int -TkLineToArea(end1Ptr, end2Ptr, rectPtr) - double end1Ptr[2]; /* X and y coordinates for one endpoint - * of line. */ - double end2Ptr[2]; /* X and y coordinates for other endpoint - * of line. */ - double rectPtr[4]; /* Points to coords for rectangle, in the - * order x1, y1, x2, y2. X1 must be no - * larger than x2, and y1 no larger than y2. */ +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. + * 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]) @@ -177,17 +174,16 @@ TkLineToArea(end1Ptr, end2Ptr, rectPtr) } /* - * 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. + * 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])) { @@ -197,7 +193,7 @@ TkLineToArea(end1Ptr, end2Ptr, rectPtr) /* * Horizontal line. */ - + if (((end1Ptr[0] >= rectPtr[0]) ^ (end2Ptr[0] >= rectPtr[0])) && (end1Ptr[1] >= rectPtr[1]) && (end1Ptr[1] <= rectPtr[3])) { @@ -205,59 +201,63 @@ TkLineToArea(end1Ptr, end2Ptr, rectPtr) } } 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. + * 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]; + low = end1Ptr[0]; + high = end2Ptr[0]; } else { - low = end2Ptr[0]; high = end1Ptr[0]; + 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]; + low = end1Ptr[1]; + high = end2Ptr[1]; } else { - low = end2Ptr[1]; high = end1Ptr[1]; + 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)) { @@ -272,14 +272,13 @@ TkLineToArea(end1Ptr, end2Ptr, rectPtr) * * TkThickPolyLineToArea -- * - * This procedure is called to determine whether a connected - * series of line segments lies entirely inside, entirely - * outside, or overlapping a given rectangular area. + * 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. + * -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. @@ -289,28 +288,27 @@ TkLineToArea(end1Ptr, end2Ptr, rectPtr) /* ARGSUSED */ int -TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) - double *coordPtr; /* Points to an array of coordinates for - * the polyline: x0, y0, x1, y1, ... */ - int numPoints; /* Total number of points at *coordPtr. */ - double width; /* Width of each line segment. */ - int capStyle; /* How are end-points of polyline drawn? +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? + int joinStyle, /* How are joints in polyline drawn? * JoinMiter, JoinRound, or JoinBevel. */ - double *rectPtr; /* Rectangular area to check against. */ + 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. */ + 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; @@ -321,19 +319,16 @@ TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) } /* - * 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. + * 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 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)) @@ -348,9 +343,9 @@ TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) } /* - * 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. + * 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) { @@ -365,10 +360,10 @@ TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) 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 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) { @@ -401,8 +396,7 @@ TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) } /* - * If caps are rounded, check the cap around the final point - * of the line. + * If caps are rounded, check the cap around the final point of the line. */ if (capStyle == CapRound) { @@ -426,10 +420,9 @@ TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) * 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. + * 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. @@ -438,15 +431,15 @@ TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr) */ double -TkPolygonToPoint(polyPtr, numPoints, pointPtr) - double *polyPtr; /* Points to an array coordinates for - * closed polygon: x0, y0, x1, y1, ... - * The polygon may be self-intersecting. */ - int numPoints; /* Total number of points at *polyPtr. */ - double *pointPtr; /* Points to coords for point. */ +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. */ + 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. */ @@ -454,13 +447,12 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) register double *pPtr; /* - * Iterate through all of the edges in the polygon, updating - * bestDist and intersections. + * 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. + * 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; @@ -470,10 +462,9 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) 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. + * 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]) { @@ -514,13 +505,13 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) } } else { double m1, b1, m2, b2; - int lower; /* Non-zero means point below line. */ + 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. + * 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]); @@ -554,8 +545,8 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) } /* - * Compute the distance to the closest point, and see if that - * is the best distance seen so far. + * 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); @@ -565,8 +556,8 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) } /* - * We've processed all of the points. If the number of intersections - * is odd, the point is inside the polygon. + * We've processed all of the points. If the number of intersections is + * odd, the point is inside the polygon. */ if (intersections & 0x1) { @@ -580,14 +571,14 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) * * TkPolygonToArea -- * - * Determine whether a polygon lies entirely inside, entirely - * outside, or overlapping a given rectangular area. + * 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. + * -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. @@ -596,14 +587,14 @@ TkPolygonToPoint(polyPtr, numPoints, pointPtr) */ int -TkPolygonToArea(polyPtr, numPoints, rectPtr) - double *polyPtr; /* Points to an array coordinates for - * closed polygon: x0, y0, x1, y1, ... - * The polygon may be self-intersecting. */ - int numPoints; /* Total number of points at *polyPtr. */ - register double *rectPtr; /* Points to coords for rectangle, in the - * order x1, y1, x2, y2. X1 and y1 must - * be lower-left corner. */ +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 @@ -612,9 +603,8 @@ TkPolygonToArea(polyPtr, numPoints, rectPtr) 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". + * 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); @@ -629,10 +619,10 @@ TkPolygonToArea(polyPtr, numPoints, rectPtr) } /* - * 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 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) { @@ -649,17 +639,16 @@ TkPolygonToArea(polyPtr, numPoints, rectPtr) * * TkOvalToPoint -- * - * Computes the distance from a given point to a given - * oval, in canvas units. + * 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. + * 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. @@ -669,22 +658,23 @@ TkPolygonToArea(polyPtr, numPoints, rectPtr) /* ARGSUSED */ double -TkOvalToPoint(ovalPtr, width, filled, pointPtr) - double ovalPtr[4]; /* Pointer to array of four coordinates - * (x1, y1, x2, y2) defining oval's bounding +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 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. + * 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); @@ -693,16 +683,14 @@ TkOvalToPoint(ovalPtr, width, filled, pointPtr) 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. + * 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. + * 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) { @@ -710,11 +698,11 @@ TkOvalToPoint(ovalPtr, width, filled, pointPtr) } /* - * 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. + * 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) { @@ -725,9 +713,9 @@ TkOvalToPoint(ovalPtr, width, filled, pointPtr) - 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. + * 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]; @@ -750,14 +738,14 @@ TkOvalToPoint(ovalPtr, width, filled, pointPtr) * * TkOvalToArea -- * - * Determine whether an oval lies entirely inside, entirely - * outside, or overlapping a given rectangular area. + * 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. + * -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. @@ -766,20 +754,20 @@ TkOvalToPoint(ovalPtr, width, filled, pointPtr) */ int -TkOvalToArea(ovalPtr, rectPtr) - register double *ovalPtr; /* Points to coordinates definining the +TkOvalToArea( + register double *ovalPtr, /* Points to coordinates definining the * bounding rectangle for the oval: x1, y1, - * x2, y2. X1 must be less than x2 and y1 - * less than y2. */ - register double *rectPtr; /* Points to coords for rectangle, in the - * order x1, y1, x2, y2. X1 and y1 must - * be lower-left corner. */ + * 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. + * First, see if oval is entirely inside rectangle or entirely outside + * rectangle. */ if ((rectPtr[0] <= ovalPtr[0]) && (rectPtr[2] >= ovalPtr[2]) @@ -792,11 +780,10 @@ TkOvalToArea(ovalPtr, rectPtr) } /* - * 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. + * 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; @@ -872,8 +859,8 @@ TkOvalToArea(ovalPtr, rectPtr) * * TkIncludePoint -- * - * Given a point and a generic canvas item header, expand - * the item's bounding box if needed to include the point. + * Given a point and a generic canvas item header, expand the item's + * bounding box if needed to include the point. * * Results: * None. @@ -886,11 +873,11 @@ TkOvalToArea(ovalPtr, rectPtr) /* ARGSUSED */ void -TkIncludePoint(itemPtr, pointPtr) - register Tk_Item *itemPtr; /* Item whose bounding box is - * being calculated. */ - double *pointPtr; /* Address of two doubles giving - * x and y coordinates of point. */ +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; @@ -915,15 +902,14 @@ TkIncludePoint(itemPtr, pointPtr) * * TkBezierScreenPoints -- * - * Given four control points, create a larger set of XPoints - * for a Bezier spline based on the points. + * 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. + * 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. @@ -932,15 +918,12 @@ TkIncludePoint(itemPtr, pointPtr) */ void -TkBezierScreenPoints(canvas, control, numSteps, xPointPtr) - Tk_Canvas canvas; /* Canvas in which curve is to be - * drawn. */ - double control[]; /* Array of coordinates for four - * control points: x0, y0, x1, y1, - * ... x3 y3. */ - int numSteps; /* Number of curve points to - * generate. */ - register XPoint *xPointPtr; /* Where to put new points. */ +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; @@ -966,15 +949,14 @@ TkBezierScreenPoints(canvas, control, numSteps, xPointPtr) * * TkBezierPoints -- * - * Given four control points, create a larger set of points - * for a Bezier spline based on the points. + * 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. + * 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. @@ -983,13 +965,11 @@ TkBezierScreenPoints(canvas, control, numSteps, xPointPtr) */ void -TkBezierPoints(control, numSteps, coordPtr) - double control[]; /* Array of coordinates for four - * control points: x0, y0, x1, y1, - * ... x3 y3. */ - int numSteps; /* Number of curve points to - * generate. */ - register double *coordPtr; /* Where to put new points. */ +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; @@ -1013,20 +993,21 @@ TkBezierPoints(control, numSteps, coordPtr) * * 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. + * Given a set of points, create a new set of points that fit parabolic + * splines to the line segments connecting the original points. Produces + * output points in either of two forms. * - * Note: in spite of this procedure's name, it does *not* generate - * Bezier curves. Since only three control points are used for - * each curve segment, not four, the curves are actually just - * parabolic. + * 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. + * 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. @@ -1035,40 +1016,40 @@ TkBezierPoints(control, numSteps, coordPtr) */ int -TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints) - Tk_Canvas canvas; /* Canvas in which curve is to be - * drawn. */ - double *pointPtr; /* Array of input coordinates: x0, - * y0, x1, y1, etc.. */ - int numPoints; /* Number of points at pointPtr. */ - int numSteps; /* Number of steps to use for each - * spline segments (determines - * smoothness of curve). */ - XPoint xPoints[]; /* Array of XPoints to fill in (e.g. - * for display. NULL means don't - * fill in any XPoints. */ - double dblPoints[]; /* Array of points to fill in as - * doubles, in the form x0, y0, - * x1, y1, .... NULL means don't - * fill in anything in this form. - * Caller must make sure that this - * array has enough space. */ +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 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. */ + /* + * 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; } @@ -1114,9 +1095,8 @@ TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints) 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. + * 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) { @@ -1132,9 +1112,8 @@ TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints) } /* - * Set up the last two control points. This is done - * differently for the last spline of an open curve - * than for other cases. + * 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) { @@ -1150,10 +1129,9 @@ TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints) } /* - * 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 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])) @@ -1194,14 +1172,193 @@ TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints) /* *-------------------------------------------------------------- * + * 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 procedure generates Postscript commands that create - * a path corresponding to a given Bezier curve. + * 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. + * None. Postscript commands to generate the path are appended to the + * interp's result. * * Side effects: * None. @@ -1210,14 +1367,14 @@ TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints) */ void -TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) - Tcl_Interp *interp; /* Interpreter in whose result the - * Postscript is to be stored. */ - Tk_Canvas canvas; /* Canvas widget for which the - * Postscript is being generated. */ - double *pointPtr; /* Array of input coordinates: x0, - * y0, x1, y1, etc.. */ - int numPoints; /* Number of points at pointPtr. */ +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; @@ -1225,9 +1382,9 @@ TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) char buffer[200]; /* - * If the curve is a closed one then generate a special spline - * that spans the last points and the first ones. Otherwise - * just put the first point into the path. + * If 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]) @@ -1253,11 +1410,11 @@ TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) sprintf(buffer, "%.15g %.15g moveto\n", control[6], Tk_CanvasPsY(canvas, control[7])); } - Tcl_AppendResult(interp, buffer, (char *) NULL); + Tcl_AppendResult(interp, buffer, NULL); /* - * Cycle through all the remaining points in the curve, generating - * a curve section for each vertex in the linear path. + * 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) { @@ -1265,9 +1422,8 @@ TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) 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. + * 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) { @@ -1284,7 +1440,115 @@ TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) control[2], Tk_CanvasPsY(canvas, control[3]), control[4], Tk_CanvasPsY(canvas, control[5]), control[6], Tk_CanvasPsY(canvas, control[7])); - Tcl_AppendResult(interp, buffer, (char *) NULL); + Tcl_AppendResult(interp, buffer, NULL); + } +} + +/* + *-------------------------------------------------------------- + * + * 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; + char buffer[200]; + + /* + * Put the first point into the path. + */ + + sprintf(buffer, "%.15g %.15g moveto\n", + pointPtr[0], Tk_CanvasPsY(canvas, pointPtr[1])); + Tcl_AppendResult(interp, buffer, NULL); + + /* + * 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. + */ + + sprintf(buffer, "%.15g %.15g lineto\n", + segPtr[6], Tk_CanvasPsY(canvas, segPtr[7])); + } else { + /* + * This is a generic Bezier curve segment. + */ + + sprintf(buffer, "%.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])); + } + Tcl_AppendResult(interp, buffer, NULL); + } + + /* + * 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. + */ + + sprintf(buffer, "%.15g %.15g lineto\n", + control[6], Tk_CanvasPsY(canvas, control[7])); + } else { + /* + * Bezier curve segment. + */ + + sprintf(buffer, "%.15g %.15g %.15g %.15g %.15g %.15g curveto\n", + control[2], Tk_CanvasPsY(canvas, control[3]), + control[4], Tk_CanvasPsY(canvas, control[5]), + control[6], Tk_CanvasPsY(canvas, control[7])); + } + Tcl_AppendResult(interp, buffer, NULL); } } @@ -1293,16 +1557,14 @@ TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) * * 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. + * 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 + * 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: @@ -1312,36 +1574,39 @@ TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints) */ int -TkGetMiterPoints(p1, p2, p3, width, m1, m2) - double p1[]; /* Points to x- and y-coordinates of point +TkGetMiterPoints( + double p1[], /* Points to x- and y-coordinates of point * before vertex. */ - double p2[]; /* Points to x- and y-coordinates of vertex + double p2[], /* Points to x- and y-coordinates of vertex * for mitered joint. */ - double p3[]; /* Points to x- and y-coordinates of point + 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 + 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 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 deltaX, deltaY; /* X and y offsets cooresponding to dist + * (fudge factors for bounding box). */ double p1x, p1y, p2x, p2y, p3x, p3y; - static double elevenDegrees = (11.0*2.0*PI)/360.0; +#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. + * 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); @@ -1358,6 +1623,7 @@ TkGetMiterPoints(p1, p2, p3, width, m1, m2) } else { theta1 = atan2(p1y - p2y, p1x - p2x); } + if (p3y == p2y) { theta2 = (p3x > p2x) ? 0 : PI; } else if (p3x == p2x) { @@ -1365,23 +1631,26 @@ TkGetMiterPoints(p1, p2, p3, width, m1, m2) } 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). + * Compute theta3 (make sure that it points to the left when looking from + * p1 to p2). */ theta3 = (theta1 + theta2)/2.0; @@ -1394,6 +1663,7 @@ TkGetMiterPoints(p1, p2, p3, width, m1, m2) deltaY = dist*sin(theta3); m1[1] = p2y + deltaY; m2[1] = p2y - deltaY; + return 1; } @@ -1402,13 +1672,13 @@ TkGetMiterPoints(p1, p2, p3, width, m1, m2) * * 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. + * 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: + * There is no return value. M1 and m2 are filled in to correspond to m1 + * and m2 in the diagram below: * * ----------------* m1 * | @@ -1416,9 +1686,9 @@ TkGetMiterPoints(p1, p2, p3, width, m1, m2) * | * ----------------* 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 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 | @@ -1435,17 +1705,17 @@ TkGetMiterPoints(p1, p2, p3, width, m1, m2) */ void -TkGetButtPoints(p1, p2, width, project, m1, m2) - double p1[]; /* Points to x- and y-coordinates of point +TkGetButtPoints( + double p1[], /* Points to x- and y-coordinates of point * before vertex. */ - double p2[]; /* Points to x- and y-coordinates of 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 + 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 + 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. */ @@ -1471,3 +1741,11 @@ TkGetButtPoints(p1, p2, width, project, m1, m2) } } } + +/* + * Local Variables: + * mode: c + * c-basic-offset: 4 + * fill-column: 78 + * End: + */ |