1450 lines
39 KiB
C
1450 lines
39 KiB
C
/*
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* tkTrig.c --
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*
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* This file contains a collection of trigonometry utility
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* routines that are used by Tk and in particular by the
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* canvas code. It also has miscellaneous geometry functions
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* used by canvases.
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*
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* Copyright (c) 1992-1994 The Regents of the University of California.
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* Copyright (c) 1994 Sun Microsystems, Inc.
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*
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* See the file "license.terms" for information on usage and redistribution
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* of this file, and for a DISCLAIMER OF ALL WARRANTIES.
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*
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* SCCS: @(#) tkTrig.c 1.23 96/02/15 18:53:05
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*/
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#include <stdio.h>
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#include "tkInt.h"
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#include "tkPort.h"
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#include "tkCanvas.h"
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#undef MIN
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#define MIN(a,b) (((a) < (b)) ? (a) : (b))
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#undef MAX
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#define MAX(a,b) (((a) > (b)) ? (a) : (b))
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#ifndef PI
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# define PI 3.14159265358979323846
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#endif /* PI */
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/*
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*--------------------------------------------------------------
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*
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* TkLineToPoint --
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*
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* Compute the distance from a point to a finite line segment.
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*
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* Results:
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* The return value is the distance from the line segment
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* whose end-points are *end1Ptr and *end2Ptr to the point
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* given by *pointPtr.
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*
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* Side effects:
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* None.
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*
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*--------------------------------------------------------------
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*/
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double
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TkLineToPoint(end1Ptr, end2Ptr, pointPtr)
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double end1Ptr[2]; /* Coordinates of first end-point of line. */
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double end2Ptr[2]; /* Coordinates of second end-point of line. */
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double pointPtr[2]; /* Points to coords for point. */
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{
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double x, y;
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/*
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* Compute the point on the line that is closest to the
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* point. This must be done separately for vertical edges,
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* horizontal edges, and other edges.
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*/
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if (end1Ptr[0] == end2Ptr[0]) {
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/*
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* Vertical edge.
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*/
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x = end1Ptr[0];
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if (end1Ptr[1] >= end2Ptr[1]) {
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y = MIN(end1Ptr[1], pointPtr[1]);
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y = MAX(y, end2Ptr[1]);
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} else {
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y = MIN(end2Ptr[1], pointPtr[1]);
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y = MAX(y, end1Ptr[1]);
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}
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} else if (end1Ptr[1] == end2Ptr[1]) {
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/*
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* Horizontal edge.
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*/
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y = end1Ptr[1];
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if (end1Ptr[0] >= end2Ptr[0]) {
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x = MIN(end1Ptr[0], pointPtr[0]);
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x = MAX(x, end2Ptr[0]);
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} else {
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x = MIN(end2Ptr[0], pointPtr[0]);
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x = MAX(x, end1Ptr[0]);
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}
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} else {
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double m1, b1, m2, b2;
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/*
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* The edge is neither horizontal nor vertical. Convert the
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* edge to a line equation of the form y = m1*x + b1. Then
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* compute a line perpendicular to this edge but passing
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* through the point, also in the form y = m2*x + b2.
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*/
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m1 = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]);
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b1 = end1Ptr[1] - m1*end1Ptr[0];
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m2 = -1.0/m1;
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b2 = pointPtr[1] - m2*pointPtr[0];
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x = (b2 - b1)/(m1 - m2);
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y = m1*x + b1;
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if (end1Ptr[0] > end2Ptr[0]) {
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if (x > end1Ptr[0]) {
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x = end1Ptr[0];
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y = end1Ptr[1];
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} else if (x < end2Ptr[0]) {
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x = end2Ptr[0];
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y = end2Ptr[1];
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}
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} else {
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if (x > end2Ptr[0]) {
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x = end2Ptr[0];
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y = end2Ptr[1];
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} else if (x < end1Ptr[0]) {
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x = end1Ptr[0];
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y = end1Ptr[1];
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}
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}
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}
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/*
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* Compute the distance to the closest point.
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*/
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return hypot(pointPtr[0] - x, pointPtr[1] - y);
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}
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/*
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*--------------------------------------------------------------
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*
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* TkLineToArea --
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*
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* Determine whether a line lies entirely inside, entirely
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* outside, or overlapping a given rectangular area.
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*
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* Results:
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* -1 is returned if the line given by end1Ptr and end2Ptr
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* is entirely outside the rectangle given by rectPtr. 0 is
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* returned if the polygon overlaps the rectangle, and 1 is
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* returned if the polygon is entirely inside the rectangle.
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*
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* Side effects:
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* None.
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*
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*--------------------------------------------------------------
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*/
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int
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TkLineToArea(end1Ptr, end2Ptr, rectPtr)
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double end1Ptr[2]; /* X and y coordinates for one endpoint
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* of line. */
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double end2Ptr[2]; /* X and y coordinates for other endpoint
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* of line. */
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double rectPtr[4]; /* Points to coords for rectangle, in the
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* order x1, y1, x2, y2. X1 must be no
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* larger than x2, and y1 no larger than y2. */
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{
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int inside1, inside2;
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/*
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* First check the two points individually to see whether they
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* are inside the rectangle or not.
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*/
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inside1 = (end1Ptr[0] >= rectPtr[0]) && (end1Ptr[0] <= rectPtr[2])
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&& (end1Ptr[1] >= rectPtr[1]) && (end1Ptr[1] <= rectPtr[3]);
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inside2 = (end2Ptr[0] >= rectPtr[0]) && (end2Ptr[0] <= rectPtr[2])
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&& (end2Ptr[1] >= rectPtr[1]) && (end2Ptr[1] <= rectPtr[3]);
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if (inside1 != inside2) {
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return 0;
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}
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if (inside1 & inside2) {
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return 1;
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}
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/*
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* Both points are outside the rectangle, but still need to check
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* for intersections between the line and the rectangle. Horizontal
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* and vertical lines are particularly easy, so handle them
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* separately.
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*/
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if (end1Ptr[0] == end2Ptr[0]) {
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/*
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* Vertical line.
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*/
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if (((end1Ptr[1] >= rectPtr[1]) ^ (end2Ptr[1] >= rectPtr[1]))
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&& (end1Ptr[0] >= rectPtr[0])
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&& (end1Ptr[0] <= rectPtr[2])) {
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return 0;
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}
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} else if (end1Ptr[1] == end2Ptr[1]) {
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/*
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* Horizontal line.
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*/
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if (((end1Ptr[0] >= rectPtr[0]) ^ (end2Ptr[0] >= rectPtr[0]))
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&& (end1Ptr[1] >= rectPtr[1])
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&& (end1Ptr[1] <= rectPtr[3])) {
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return 0;
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}
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} else {
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double m, x, y, low, high;
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/*
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* Diagonal line. Compute slope of line and use
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* for intersection checks against each of the
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* sides of the rectangle: left, right, bottom, top.
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*/
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m = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]);
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if (end1Ptr[0] < end2Ptr[0]) {
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low = end1Ptr[0]; high = end2Ptr[0];
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} else {
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low = end2Ptr[0]; high = end1Ptr[0];
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}
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/*
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* Left edge.
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*/
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y = end1Ptr[1] + (rectPtr[0] - end1Ptr[0])*m;
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if ((rectPtr[0] >= low) && (rectPtr[0] <= high)
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&& (y >= rectPtr[1]) && (y <= rectPtr[3])) {
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return 0;
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}
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/*
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* Right edge.
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*/
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y += (rectPtr[2] - rectPtr[0])*m;
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if ((y >= rectPtr[1]) && (y <= rectPtr[3])
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&& (rectPtr[2] >= low) && (rectPtr[2] <= high)) {
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return 0;
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}
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/*
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* Bottom edge.
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*/
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if (end1Ptr[1] < end2Ptr[1]) {
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low = end1Ptr[1]; high = end2Ptr[1];
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} else {
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low = end2Ptr[1]; high = end1Ptr[1];
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}
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x = end1Ptr[0] + (rectPtr[1] - end1Ptr[1])/m;
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if ((x >= rectPtr[0]) && (x <= rectPtr[2])
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&& (rectPtr[1] >= low) && (rectPtr[1] <= high)) {
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return 0;
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}
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/*
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* Top edge.
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*/
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x += (rectPtr[3] - rectPtr[1])/m;
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if ((x >= rectPtr[0]) && (x <= rectPtr[2])
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&& (rectPtr[3] >= low) && (rectPtr[3] <= high)) {
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return 0;
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}
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}
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return -1;
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}
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/*
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*--------------------------------------------------------------
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*
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* TkThickPolyLineToArea --
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*
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* This procedure is called to determine whether a connected
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* series of line segments lies entirely inside, entirely
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* outside, or overlapping a given rectangular area.
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*
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* Results:
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* -1 is returned if the lines are entirely outside the area,
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* 0 if they overlap, and 1 if they are entirely inside the
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* given area.
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*
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* Side effects:
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* None.
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*
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*--------------------------------------------------------------
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*/
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/* ARGSUSED */
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int
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TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr)
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double *coordPtr; /* Points to an array of coordinates for
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* the polyline: x0, y0, x1, y1, ... */
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int numPoints; /* Total number of points at *coordPtr. */
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double width; /* Width of each line segment. */
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int capStyle; /* How are end-points of polyline drawn?
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* CapRound, CapButt, or CapProjecting. */
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int joinStyle; /* How are joints in polyline drawn?
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* JoinMiter, JoinRound, or JoinBevel. */
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double *rectPtr; /* Rectangular area to check against. */
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{
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double radius, poly[10];
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int count;
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int changedMiterToBevel; /* Non-zero means that a mitered corner
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* had to be treated as beveled after all
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* because the angle was < 11 degrees. */
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int inside; /* Tentative guess about what to return,
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* based on all points seen so far: one
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* means everything seen so far was
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* inside the area; -1 means everything
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* was outside the area. 0 means overlap
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* has been found. */
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radius = width/2.0;
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inside = -1;
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if ((coordPtr[0] >= rectPtr[0]) && (coordPtr[0] <= rectPtr[2])
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&& (coordPtr[1] >= rectPtr[1]) && (coordPtr[1] <= rectPtr[3])) {
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inside = 1;
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}
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/*
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* Iterate through all of the edges of the line, computing a polygon
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* for each edge and testing the area against that polygon. In
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* addition, there are additional tests to deal with rounded joints
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* and caps.
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*/
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changedMiterToBevel = 0;
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for (count = numPoints; count >= 2; count--, coordPtr += 2) {
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/*
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* If rounding is done around the first point of the edge
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* then test a circular region around the point with the
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* area.
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*/
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if (((capStyle == CapRound) && (count == numPoints))
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|| ((joinStyle == JoinRound) && (count != numPoints))) {
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poly[0] = coordPtr[0] - radius;
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poly[1] = coordPtr[1] - radius;
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poly[2] = coordPtr[0] + radius;
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poly[3] = coordPtr[1] + radius;
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if (TkOvalToArea(poly, rectPtr) != inside) {
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return 0;
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}
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}
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/*
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* Compute the polygonal shape corresponding to this edge,
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* consisting of two points for the first point of the edge
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* and two points for the last point of the edge.
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*/
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if (count == numPoints) {
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TkGetButtPoints(coordPtr+2, coordPtr, width,
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capStyle == CapProjecting, poly, poly+2);
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} else if ((joinStyle == JoinMiter) && !changedMiterToBevel) {
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poly[0] = poly[6];
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poly[1] = poly[7];
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poly[2] = poly[4];
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poly[3] = poly[5];
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} else {
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TkGetButtPoints(coordPtr+2, coordPtr, width, 0, poly, poly+2);
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/*
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* If the last joint was beveled, then also check a
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* polygon comprising the last two points of the previous
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* polygon and the first two from this polygon; this checks
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* the wedges that fill the beveled joint.
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*/
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if ((joinStyle == JoinBevel) || changedMiterToBevel) {
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poly[8] = poly[0];
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poly[9] = poly[1];
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if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
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return 0;
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}
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changedMiterToBevel = 0;
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}
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}
|
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if (count == 2) {
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TkGetButtPoints(coordPtr, coordPtr+2, width,
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capStyle == CapProjecting, poly+4, poly+6);
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} else if (joinStyle == JoinMiter) {
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if (TkGetMiterPoints(coordPtr, coordPtr+2, coordPtr+4,
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(double) width, poly+4, poly+6) == 0) {
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changedMiterToBevel = 1;
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TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4,
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poly+6);
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}
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} else {
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TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4, poly+6);
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}
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poly[8] = poly[0];
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poly[9] = poly[1];
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if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
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return 0;
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}
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}
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/*
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* If caps are rounded, check the cap around the final point
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* of the line.
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*/
|
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if (capStyle == CapRound) {
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poly[0] = coordPtr[0] - radius;
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poly[1] = coordPtr[1] - radius;
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poly[2] = coordPtr[0] + radius;
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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(polyPtr, numPoints, pointPtr)
|
||
double *polyPtr; /* Points to an array coordinates for
|
||
* closed polygon: x0, y0, x1, y1, ...
|
||
* The polygon may be self-intersecting. */
|
||
int numPoints; /* Total number of points at *polyPtr. */
|
||
double *pointPtr; /* Points to coords for point. */
|
||
{
|
||
double bestDist; /* Closest distance between point and
|
||
* any edge in polygon. */
|
||
int intersections; /* Number of edges in the polygon that
|
||
* intersect a ray extending vertically
|
||
* upwards from the point to infinity. */
|
||
int count;
|
||
register double *pPtr;
|
||
|
||
/*
|
||
* Iterate through all of the edges in the polygon, updating
|
||
* bestDist and intersections.
|
||
*
|
||
* TRICKY POINT: when computing intersections, include left
|
||
* x-coordinate of line within its range, but not y-coordinate.
|
||
* Otherwise if the point lies exactly below a vertex we'll
|
||
* count it as two intersections.
|
||
*/
|
||
|
||
bestDist = 1.0e36;
|
||
intersections = 0;
|
||
|
||
for (count = numPoints, pPtr = polyPtr; count > 1; count--, pPtr += 2) {
|
||
double x, y, dist;
|
||
|
||
/*
|
||
* Compute the point on the current edge closest to the point
|
||
* and update the intersection count. This must be done
|
||
* separately for vertical edges, horizontal edges, and
|
||
* other edges.
|
||
*/
|
||
|
||
if (pPtr[2] == pPtr[0]) {
|
||
|
||
/*
|
||
* Vertical edge.
|
||
*/
|
||
|
||
x = pPtr[0];
|
||
if (pPtr[1] >= pPtr[3]) {
|
||
y = MIN(pPtr[1], pointPtr[1]);
|
||
y = MAX(y, pPtr[3]);
|
||
} else {
|
||
y = MIN(pPtr[3], pointPtr[1]);
|
||
y = MAX(y, pPtr[1]);
|
||
}
|
||
} else if (pPtr[3] == pPtr[1]) {
|
||
|
||
/*
|
||
* Horizontal edge.
|
||
*/
|
||
|
||
y = pPtr[1];
|
||
if (pPtr[0] >= pPtr[2]) {
|
||
x = MIN(pPtr[0], pointPtr[0]);
|
||
x = MAX(x, pPtr[2]);
|
||
if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[0])
|
||
&& (pointPtr[0] >= pPtr[2])) {
|
||
intersections++;
|
||
}
|
||
} else {
|
||
x = MIN(pPtr[2], pointPtr[0]);
|
||
x = MAX(x, pPtr[0]);
|
||
if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[2])
|
||
&& (pointPtr[0] >= pPtr[0])) {
|
||
intersections++;
|
||
}
|
||
}
|
||
} else {
|
||
double m1, b1, m2, b2;
|
||
int lower; /* Non-zero means point below line. */
|
||
|
||
/*
|
||
* The edge is neither horizontal nor vertical. Convert the
|
||
* edge to a line equation of the form y = m1*x + b1. Then
|
||
* compute a line perpendicular to this edge but passing
|
||
* through the point, also in the form y = m2*x + b2.
|
||
*/
|
||
|
||
m1 = (pPtr[3] - pPtr[1])/(pPtr[2] - pPtr[0]);
|
||
b1 = pPtr[1] - m1*pPtr[0];
|
||
m2 = -1.0/m1;
|
||
b2 = pointPtr[1] - m2*pointPtr[0];
|
||
x = (b2 - b1)/(m1 - m2);
|
||
y = m1*x + b1;
|
||
if (pPtr[0] > pPtr[2]) {
|
||
if (x > pPtr[0]) {
|
||
x = pPtr[0];
|
||
y = pPtr[1];
|
||
} else if (x < pPtr[2]) {
|
||
x = pPtr[2];
|
||
y = pPtr[3];
|
||
}
|
||
} else {
|
||
if (x > pPtr[2]) {
|
||
x = pPtr[2];
|
||
y = pPtr[3];
|
||
} else if (x < pPtr[0]) {
|
||
x = pPtr[0];
|
||
y = pPtr[1];
|
||
}
|
||
}
|
||
lower = (m1*pointPtr[0] + b1) > pointPtr[1];
|
||
if (lower && (pointPtr[0] >= MIN(pPtr[0], pPtr[2]))
|
||
&& (pointPtr[0] < MAX(pPtr[0], pPtr[2]))) {
|
||
intersections++;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Compute the distance to the closest point, and see if that
|
||
* is the best distance seen so far.
|
||
*/
|
||
|
||
dist = hypot(pointPtr[0] - x, pointPtr[1] - y);
|
||
if (dist < bestDist) {
|
||
bestDist = dist;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* We've processed all of the points. If the number of intersections
|
||
* is odd, the point is inside the polygon.
|
||
*/
|
||
|
||
if (intersections & 0x1) {
|
||
return 0.0;
|
||
}
|
||
return bestDist;
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkPolygonToArea --
|
||
*
|
||
* Determine whether a polygon lies entirely inside, entirely
|
||
* outside, or overlapping a given rectangular area.
|
||
*
|
||
* Results:
|
||
* -1 is returned if the polygon given by polyPtr and numPoints
|
||
* is entirely outside the rectangle given by rectPtr. 0 is
|
||
* returned if the polygon overlaps the rectangle, and 1 is
|
||
* returned if the polygon is entirely inside the rectangle.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
TkPolygonToArea(polyPtr, numPoints, rectPtr)
|
||
double *polyPtr; /* Points to an array coordinates for
|
||
* closed polygon: x0, y0, x1, y1, ...
|
||
* The polygon may be self-intersecting. */
|
||
int numPoints; /* Total number of points at *polyPtr. */
|
||
register double *rectPtr; /* Points to coords for rectangle, in the
|
||
* order x1, y1, x2, y2. X1 and y1 must
|
||
* be lower-left corner. */
|
||
{
|
||
int state; /* State of all edges seen so far (-1 means
|
||
* outside, 1 means inside, won't ever be
|
||
* 0). */
|
||
int count;
|
||
register double *pPtr;
|
||
|
||
/*
|
||
* Iterate over all of the edges of the polygon and test them
|
||
* against the rectangle. Can quit as soon as the state becomes
|
||
* "intersecting".
|
||
*/
|
||
|
||
state = TkLineToArea(polyPtr, polyPtr+2, rectPtr);
|
||
if (state == 0) {
|
||
return 0;
|
||
}
|
||
for (pPtr = polyPtr+2, count = numPoints-1; count >= 2;
|
||
pPtr += 2, count--) {
|
||
if (TkLineToArea(pPtr, pPtr+2, rectPtr) != state) {
|
||
return 0;
|
||
}
|
||
}
|
||
|
||
/*
|
||
* If all of the edges were inside the rectangle we're done.
|
||
* If all of the edges were outside, then the rectangle could
|
||
* still intersect the polygon (if it's entirely enclosed).
|
||
* Call TkPolygonToPoint to figure this out.
|
||
*/
|
||
|
||
if (state == 1) {
|
||
return 1;
|
||
}
|
||
if (TkPolygonToPoint(polyPtr, numPoints, rectPtr) == 0.0) {
|
||
return 0;
|
||
}
|
||
return -1;
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkOvalToPoint --
|
||
*
|
||
* Computes the distance from a given point to a given
|
||
* oval, in canvas units.
|
||
*
|
||
* Results:
|
||
* The return value is 0 if the point given by *pointPtr is
|
||
* inside the oval. If the point isn't inside the
|
||
* oval then the return value is approximately the distance
|
||
* from the point to the oval. If the oval is filled, then
|
||
* anywhere in the interior is considered "inside"; if
|
||
* the oval isn't filled, then "inside" means only the area
|
||
* occupied by the outline.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
/* ARGSUSED */
|
||
double
|
||
TkOvalToPoint(ovalPtr, width, filled, pointPtr)
|
||
double ovalPtr[4]; /* Pointer to array of four coordinates
|
||
* (x1, y1, x2, y2) defining oval's bounding
|
||
* box. */
|
||
double width; /* Width of outline for oval. */
|
||
int filled; /* Non-zero means oval should be treated as
|
||
* filled; zero means only consider outline. */
|
||
double pointPtr[2]; /* Coordinates of point. */
|
||
{
|
||
double xDelta, yDelta, scaledDistance, distToOutline, distToCenter;
|
||
double xDiam, yDiam;
|
||
|
||
/*
|
||
* Compute the distance between the center of the oval and the
|
||
* point in question, using a coordinate system where the oval
|
||
* has been transformed to a circle with unit radius.
|
||
*/
|
||
|
||
xDelta = (pointPtr[0] - (ovalPtr[0] + ovalPtr[2])/2.0);
|
||
yDelta = (pointPtr[1] - (ovalPtr[1] + ovalPtr[3])/2.0);
|
||
distToCenter = hypot(xDelta, yDelta);
|
||
scaledDistance = hypot(xDelta / ((ovalPtr[2] + width - ovalPtr[0])/2.0),
|
||
yDelta / ((ovalPtr[3] + width - ovalPtr[1])/2.0));
|
||
|
||
|
||
/*
|
||
* If the scaled distance is greater than 1 then it means no
|
||
* hit. Compute the distance from the point to the edge of
|
||
* the circle, then scale this distance back to the original
|
||
* coordinate system.
|
||
*
|
||
* Note: this distance isn't completely accurate. It's only
|
||
* an approximation, and it can overestimate the correct
|
||
* distance when the oval is eccentric.
|
||
*/
|
||
|
||
if (scaledDistance > 1.0) {
|
||
return (distToCenter/scaledDistance) * (scaledDistance - 1.0);
|
||
}
|
||
|
||
/*
|
||
* Scaled distance less than 1 means the point is inside the
|
||
* outer edge of the oval. If this is a filled oval, then we
|
||
* have a hit. Otherwise, do the same computation as above
|
||
* (scale back to original coordinate system), but also check
|
||
* to see if the point is within the width of the outline.
|
||
*/
|
||
|
||
if (filled) {
|
||
return 0.0;
|
||
}
|
||
if (scaledDistance > 1E-10) {
|
||
distToOutline = (distToCenter/scaledDistance) * (1.0 - scaledDistance)
|
||
- width;
|
||
} else {
|
||
/*
|
||
* Avoid dividing by a very small number (it could cause an
|
||
* arithmetic overflow). This problem occurs if the point is
|
||
* very close to the center of the oval.
|
||
*/
|
||
|
||
xDiam = ovalPtr[2] - ovalPtr[0];
|
||
yDiam = ovalPtr[3] - ovalPtr[1];
|
||
if (xDiam < yDiam) {
|
||
distToOutline = (xDiam - width)/2;
|
||
} else {
|
||
distToOutline = (yDiam - width)/2;
|
||
}
|
||
}
|
||
|
||
if (distToOutline < 0.0) {
|
||
return 0.0;
|
||
}
|
||
return distToOutline;
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkOvalToArea --
|
||
*
|
||
* Determine whether an oval lies entirely inside, entirely
|
||
* outside, or overlapping a given rectangular area.
|
||
*
|
||
* Results:
|
||
* -1 is returned if the oval described by ovalPtr is entirely
|
||
* outside the rectangle given by rectPtr. 0 is returned if the
|
||
* oval overlaps the rectangle, and 1 is returned if the oval
|
||
* is entirely inside the rectangle.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
TkOvalToArea(ovalPtr, rectPtr)
|
||
register double *ovalPtr; /* Points to coordinates definining the
|
||
* bounding rectangle for the oval: x1, y1,
|
||
* x2, y2. X1 must be less than x2 and y1
|
||
* less than y2. */
|
||
register double *rectPtr; /* Points to coords for rectangle, in the
|
||
* order x1, y1, x2, y2. X1 and y1 must
|
||
* be lower-left corner. */
|
||
{
|
||
double centerX, centerY, radX, radY, deltaX, deltaY;
|
||
|
||
/*
|
||
* First, see if oval is entirely inside rectangle or entirely
|
||
* outside rectangle.
|
||
*/
|
||
|
||
if ((rectPtr[0] <= ovalPtr[0]) && (rectPtr[2] >= ovalPtr[2])
|
||
&& (rectPtr[1] <= ovalPtr[1]) && (rectPtr[3] >= ovalPtr[3])) {
|
||
return 1;
|
||
}
|
||
if ((rectPtr[2] < ovalPtr[0]) || (rectPtr[0] > ovalPtr[2])
|
||
|| (rectPtr[3] < ovalPtr[1]) || (rectPtr[1] > ovalPtr[3])) {
|
||
return -1;
|
||
}
|
||
|
||
/*
|
||
* Next, go through the rectangle side by side. For each side
|
||
* of the rectangle, find the point on the side that is closest
|
||
* to the oval's center, and see if that point is inside the
|
||
* oval. If at least one such point is inside the oval, then
|
||
* the rectangle intersects the oval.
|
||
*/
|
||
|
||
centerX = (ovalPtr[0] + ovalPtr[2])/2;
|
||
centerY = (ovalPtr[1] + ovalPtr[3])/2;
|
||
radX = (ovalPtr[2] - ovalPtr[0])/2;
|
||
radY = (ovalPtr[3] - ovalPtr[1])/2;
|
||
|
||
deltaY = rectPtr[1] - centerY;
|
||
if (deltaY < 0.0) {
|
||
deltaY = centerY - rectPtr[3];
|
||
if (deltaY < 0.0) {
|
||
deltaY = 0;
|
||
}
|
||
}
|
||
deltaY /= radY;
|
||
deltaY *= deltaY;
|
||
|
||
/*
|
||
* Left side:
|
||
*/
|
||
|
||
deltaX = (rectPtr[0] - centerX)/radX;
|
||
deltaX *= deltaX;
|
||
if ((deltaX + deltaY) <= 1.0) {
|
||
return 0;
|
||
}
|
||
|
||
/*
|
||
* Right side:
|
||
*/
|
||
|
||
deltaX = (rectPtr[2] - centerX)/radX;
|
||
deltaX *= deltaX;
|
||
if ((deltaX + deltaY) <= 1.0) {
|
||
return 0;
|
||
}
|
||
|
||
deltaX = rectPtr[0] - centerX;
|
||
if (deltaX < 0.0) {
|
||
deltaX = centerX - rectPtr[2];
|
||
if (deltaX < 0.0) {
|
||
deltaX = 0;
|
||
}
|
||
}
|
||
deltaX /= radX;
|
||
deltaX *= deltaX;
|
||
|
||
/*
|
||
* Bottom side:
|
||
*/
|
||
|
||
deltaY = (rectPtr[1] - centerY)/radY;
|
||
deltaY *= deltaY;
|
||
if ((deltaX + deltaY) < 1.0) {
|
||
return 0;
|
||
}
|
||
|
||
/*
|
||
* Top side:
|
||
*/
|
||
|
||
deltaY = (rectPtr[3] - centerY)/radY;
|
||
deltaY *= deltaY;
|
||
if ((deltaX + deltaY) < 1.0) {
|
||
return 0;
|
||
}
|
||
|
||
return -1;
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkIncludePoint --
|
||
*
|
||
* Given a point and a generic canvas item header, expand
|
||
* the item's bounding box if needed to include the point.
|
||
*
|
||
* Results:
|
||
* None.
|
||
*
|
||
* Side effects:
|
||
* The boudn.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
/* ARGSUSED */
|
||
void
|
||
TkIncludePoint(itemPtr, pointPtr)
|
||
register Tk_Item *itemPtr; /* Item whose bounding box is
|
||
* being calculated. */
|
||
double *pointPtr; /* Address of two doubles giving
|
||
* x and y coordinates of point. */
|
||
{
|
||
int tmp;
|
||
|
||
tmp = pointPtr[0] + 0.5;
|
||
if (tmp < itemPtr->x1) {
|
||
itemPtr->x1 = tmp;
|
||
}
|
||
if (tmp > itemPtr->x2) {
|
||
itemPtr->x2 = tmp;
|
||
}
|
||
tmp = 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 spline based on the points.
|
||
*
|
||
* Results:
|
||
* The array at *xPointPtr gets filled in with numSteps XPoints
|
||
* corresponding to the Bezier spline defined by the four
|
||
* control points. Note: no output point is generated for the
|
||
* first input point, but an output point *is* generated for
|
||
* the last input point.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
void
|
||
TkBezierScreenPoints(canvas, control, numSteps, xPointPtr)
|
||
Tk_Canvas canvas; /* Canvas in which curve is to be
|
||
* drawn. */
|
||
double control[]; /* Array of coordinates for four
|
||
* control points: x0, y0, x1, y1,
|
||
* ... x3 y3. */
|
||
int numSteps; /* Number of curve points to
|
||
* generate. */
|
||
register XPoint *xPointPtr; /* Where to put new points. */
|
||
{
|
||
int i;
|
||
double u, u2, u3, t, t2, t3;
|
||
|
||
for (i = 1; i <= numSteps; i++, xPointPtr++) {
|
||
t = ((double) i)/((double) numSteps);
|
||
t2 = t*t;
|
||
t3 = t2*t;
|
||
u = 1.0 - t;
|
||
u2 = u*u;
|
||
u3 = u2*u;
|
||
Tk_CanvasDrawableCoords(canvas,
|
||
(control[0]*u3 + 3.0 * (control[2]*t*u2 + control[4]*t2*u)
|
||
+ control[6]*t3),
|
||
(control[1]*u3 + 3.0 * (control[3]*t*u2 + control[5]*t2*u)
|
||
+ control[7]*t3),
|
||
&xPointPtr->x, &xPointPtr->y);
|
||
}
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkBezierPoints --
|
||
*
|
||
* Given four control points, create a larger set of points
|
||
* for a Bezier spline based on the points.
|
||
*
|
||
* Results:
|
||
* The array at *coordPtr gets filled in with 2*numSteps
|
||
* coordinates, which correspond to the Bezier spline defined
|
||
* by the four control points. Note: no output point is
|
||
* generated for the first input point, but an output point
|
||
* *is* generated for the last input point.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
void
|
||
TkBezierPoints(control, numSteps, coordPtr)
|
||
double control[]; /* Array of coordinates for four
|
||
* control points: x0, y0, x1, y1,
|
||
* ... x3 y3. */
|
||
int numSteps; /* Number of curve points to
|
||
* generate. */
|
||
register double *coordPtr; /* Where to put new points. */
|
||
{
|
||
int i;
|
||
double u, u2, u3, t, t2, t3;
|
||
|
||
for (i = 1; i <= numSteps; i++, coordPtr += 2) {
|
||
t = ((double) i)/((double) numSteps);
|
||
t2 = t*t;
|
||
t3 = t2*t;
|
||
u = 1.0 - t;
|
||
u2 = u*u;
|
||
u3 = u2*u;
|
||
coordPtr[0] = control[0]*u3
|
||
+ 3.0 * (control[2]*t*u2 + control[4]*t2*u) + control[6]*t3;
|
||
coordPtr[1] = control[1]*u3
|
||
+ 3.0 * (control[3]*t*u2 + control[5]*t2*u) + control[7]*t3;
|
||
}
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkMakeBezierCurve --
|
||
*
|
||
* Given a set of points, create a new set of points that
|
||
* fit Bezier splines to the line segments connecting the
|
||
* original points. Produces output points 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. Note: if the first and last points are the same, then
|
||
* a closed curve is generated.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints)
|
||
Tk_Canvas canvas; /* Canvas in which curve is to be
|
||
* drawn. */
|
||
double *pointPtr; /* Array of input coordinates: x0,
|
||
* y0, x1, y1, etc.. */
|
||
int numPoints; /* Number of points at pointPtr. */
|
||
int numSteps; /* Number of steps to use for each
|
||
* spline segments (determines
|
||
* smoothness of curve). */
|
||
XPoint xPoints[]; /* Array of XPoints to fill in (e.g.
|
||
* for display. NULL means don't
|
||
* fill in any XPoints. */
|
||
double dblPoints[]; /* Array of points to fill in as
|
||
* doubles, in the form x0, y0,
|
||
* x1, y1, .... NULL means don't
|
||
* fill in anything in this form.
|
||
* Caller must make sure that this
|
||
* array has enough space. */
|
||
{
|
||
int closed, outputPoints, i;
|
||
int numCoords = numPoints*2;
|
||
double control[8];
|
||
|
||
/*
|
||
* If the curve is a closed one then generate a special spline
|
||
* that spans the last points and the first ones. Otherwise
|
||
* just put the first point into the output.
|
||
*/
|
||
|
||
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;
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkMakeBezierPostscript --
|
||
*
|
||
* This procedure generates Postscript commands that create
|
||
* a path corresponding to a given Bezier curve.
|
||
*
|
||
* Results:
|
||
* None. Postscript commands to generate the path are appended
|
||
* to interp->result.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
void
|
||
TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints)
|
||
Tcl_Interp *interp; /* Interpreter in whose result the
|
||
* Postscript is to be stored. */
|
||
Tk_Canvas canvas; /* Canvas widget for which the
|
||
* Postscript is being generated. */
|
||
double *pointPtr; /* Array of input coordinates: x0,
|
||
* y0, x1, y1, etc.. */
|
||
int numPoints; /* Number of points at pointPtr. */
|
||
{
|
||
int closed, i;
|
||
int numCoords = numPoints*2;
|
||
double control[8];
|
||
char buffer[200];
|
||
|
||
/*
|
||
* If the curve is a closed one then generate a special spline
|
||
* that spans the last points and the first ones. Otherwise
|
||
* just put the first point into the path.
|
||
*/
|
||
|
||
if ((pointPtr[0] == pointPtr[numCoords-2])
|
||
&& (pointPtr[1] == pointPtr[numCoords-1])) {
|
||
closed = 1;
|
||
control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
|
||
control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
|
||
control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
|
||
control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
|
||
control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
|
||
control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
|
||
control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
|
||
control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
|
||
sprintf(buffer, "%.15g %.15g moveto\n%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
|
||
control[0], Tk_CanvasPsY(canvas, control[1]),
|
||
control[2], Tk_CanvasPsY(canvas, control[3]),
|
||
control[4], Tk_CanvasPsY(canvas, control[5]),
|
||
control[6], Tk_CanvasPsY(canvas, control[7]));
|
||
} else {
|
||
closed = 0;
|
||
control[6] = pointPtr[0];
|
||
control[7] = pointPtr[1];
|
||
sprintf(buffer, "%.15g %.15g moveto\n",
|
||
control[6], Tk_CanvasPsY(canvas, control[7]));
|
||
}
|
||
Tcl_AppendResult(interp, buffer, (char *) NULL);
|
||
|
||
/*
|
||
* Cycle through all the remaining points in the curve, generating
|
||
* a curve section for each vertex in the linear path.
|
||
*/
|
||
|
||
for (i = numPoints-2, pointPtr += 2; i > 0; i--, pointPtr += 2) {
|
||
control[2] = 0.333*control[6] + 0.667*pointPtr[0];
|
||
control[3] = 0.333*control[7] + 0.667*pointPtr[1];
|
||
|
||
/*
|
||
* Set up the last two control points. This is done
|
||
* differently for the last spline of an open curve
|
||
* than for other cases.
|
||
*/
|
||
|
||
if ((i == 1) && !closed) {
|
||
control[6] = pointPtr[2];
|
||
control[7] = pointPtr[3];
|
||
} else {
|
||
control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
|
||
control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
|
||
}
|
||
control[4] = 0.333*control[6] + 0.667*pointPtr[0];
|
||
control[5] = 0.333*control[7] + 0.667*pointPtr[1];
|
||
|
||
sprintf(buffer, "%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
|
||
control[2], Tk_CanvasPsY(canvas, control[3]),
|
||
control[4], Tk_CanvasPsY(canvas, control[5]),
|
||
control[6], Tk_CanvasPsY(canvas, control[7]));
|
||
Tcl_AppendResult(interp, buffer, (char *) NULL);
|
||
}
|
||
}
|
||
|
||
/*
|
||
*--------------------------------------------------------------
|
||
*
|
||
* TkGetMiterPoints --
|
||
*
|
||
* Given three points forming an angle, compute the
|
||
* coordinates of the inside and outside points of
|
||
* the mitered corner formed by a line of a given
|
||
* width at that angle.
|
||
*
|
||
* Results:
|
||
* If the angle formed by the three points is less than
|
||
* 11 degrees then 0 is returned and m1 and m2 aren't
|
||
* modified. Otherwise 1 is returned and the points at
|
||
* m1 and m2 are filled in with the positions of the points
|
||
* of the mitered corner.
|
||
*
|
||
* Side effects:
|
||
* None.
|
||
*
|
||
*--------------------------------------------------------------
|
||
*/
|
||
|
||
int
|
||
TkGetMiterPoints(p1, p2, p3, width, m1, m2)
|
||
double p1[]; /* Points to x- and y-coordinates of point
|
||
* before vertex. */
|
||
double p2[]; /* Points to x- and y-coordinates of vertex
|
||
* for mitered joint. */
|
||
double p3[]; /* Points to x- and y-coordinates of point
|
||
* after vertex. */
|
||
double width; /* Width of line. */
|
||
double m1[]; /* Points to place to put "left" vertex
|
||
* point (see as you face from p1 to p2). */
|
||
double m2[]; /* Points to place to put "right" vertex
|
||
* point. */
|
||
{
|
||
double theta1; /* Angle of segment p2-p1. */
|
||
double theta2; /* Angle of segment p2-p3. */
|
||
double theta; /* Angle between line segments (angle
|
||
* of joint). */
|
||
double theta3; /* Angle that bisects theta1 and
|
||
* theta2 and points to m1. */
|
||
double dist; /* Distance of miter points from p2. */
|
||
double deltaX, deltaY; /* X and y offsets cooresponding to
|
||
* dist (fudge factors for bounding
|
||
* box). */
|
||
static float elevenDegrees = (11.0*2.0*PI)/360.0;
|
||
|
||
if (p2[1] == p1[1]) {
|
||
theta1 = (p2[0] < p1[0]) ? 0 : PI;
|
||
} else if (p2[0] == p1[0]) {
|
||
theta1 = (p2[1] < p1[1]) ? PI/2.0 : -PI/2.0;
|
||
} else {
|
||
theta1 = atan2(p1[1] - p2[1], p1[0] - p2[0]);
|
||
}
|
||
if (p3[1] == p2[1]) {
|
||
theta2 = (p3[0] > p2[0]) ? 0 : PI;
|
||
} else if (p3[0] == p2[0]) {
|
||
theta2 = (p3[1] > p2[1]) ? PI/2.0 : -PI/2.0;
|
||
} else {
|
||
theta2 = atan2(p3[1] - p2[1], p3[0] - p2[0]);
|
||
}
|
||
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] = p2[0] + deltaX;
|
||
m2[0] = p2[0] - deltaX;
|
||
deltaY = dist*sin(theta3);
|
||
m1[1] = p2[1] + deltaY;
|
||
m2[1] = p2[1] - 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(p1, p2, width, project, m1, m2)
|
||
double p1[]; /* Points to x- and y-coordinates of point
|
||
* before vertex. */
|
||
double p2[]; /* Points to x- and y-coordinates of vertex
|
||
* for mitered joint. */
|
||
double width; /* Width of line. */
|
||
int project; /* Non-zero means project p2 by an additional
|
||
* width/2 before computing m1 and m2. */
|
||
double m1[]; /* Points to place to put "left" result
|
||
* point, as you face from p1 to p2. */
|
||
double m2[]; /* Points to place to put "right" result
|
||
* point. */
|
||
{
|
||
double length; /* Length of p1-p2 segment. */
|
||
double deltaX, deltaY; /* Increments in coords. */
|
||
|
||
width *= 0.5;
|
||
length = hypot(p2[0] - p1[0], p2[1] - p1[1]);
|
||
if (length == 0.0) {
|
||
m1[0] = m2[0] = p2[0];
|
||
m1[1] = m2[1] = p2[1];
|
||
} else {
|
||
deltaX = -width * (p2[1] - p1[1]) / length;
|
||
deltaY = width * (p2[0] - p1[0]) / length;
|
||
m1[0] = p2[0] + deltaX;
|
||
m2[0] = p2[0] - deltaX;
|
||
m1[1] = p2[1] + deltaY;
|
||
m2[1] = p2[1] - deltaY;
|
||
if (project) {
|
||
m1[0] += deltaY;
|
||
m2[0] += deltaY;
|
||
m1[1] -= deltaX;
|
||
m2[1] -= deltaX;
|
||
}
|
||
}
|
||
}
|