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/* $Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/tk_base/tktrig.c,v 1.1.1.1 2001/06/13 05:11:18 dtashley Exp $ */
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/*
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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) 1994-1997 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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* RCS: @(#) $Id: tktrig.c,v 1.1.1.1 2001/06/13 05:11:18 dtashley Exp $
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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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341 |
*/
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342 |
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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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349 |
if (TkOvalToArea(poly, rectPtr) != inside) {
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350 |
return 0;
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351 |
}
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352 |
}
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353 |
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354 |
/*
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355 |
* Compute the polygonal shape corresponding to this edge,
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356 |
* consisting of two points for the first point of the edge
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357 |
* and two points for the last point of the edge.
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*/
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359 |
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360 |
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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364 |
poly[0] = poly[6];
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poly[1] = poly[7];
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366 |
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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370 |
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371 |
/*
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372 |
* If the last joint was beveled, then also check a
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373 |
* polygon comprising the last two points of the previous
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374 |
* polygon and the first two from this polygon; this checks
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375 |
* the wedges that fill the beveled joint.
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*/
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377 |
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378 |
if ((joinStyle == JoinBevel) || changedMiterToBevel) {
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379 |
poly[8] = poly[0];
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380 |
poly[9] = poly[1];
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381 |
if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
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382 |
return 0;
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383 |
}
|
384 |
changedMiterToBevel = 0;
|
385 |
}
|
386 |
}
|
387 |
if (count == 2) {
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388 |
TkGetButtPoints(coordPtr, coordPtr+2, width,
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capStyle == CapProjecting, poly+4, poly+6);
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390 |
} else if (joinStyle == JoinMiter) {
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391 |
if (TkGetMiterPoints(coordPtr, coordPtr+2, coordPtr+4,
|
392 |
(double) width, poly+4, poly+6) == 0) {
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393 |
changedMiterToBevel = 1;
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394 |
TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4,
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395 |
poly+6);
|
396 |
}
|
397 |
} else {
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398 |
TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4, poly+6);
|
399 |
}
|
400 |
poly[8] = poly[0];
|
401 |
poly[9] = poly[1];
|
402 |
if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
|
403 |
return 0;
|
404 |
}
|
405 |
}
|
406 |
|
407 |
/*
|
408 |
* If caps are rounded, check the cap around the final point
|
409 |
* of the line.
|
410 |
*/
|
411 |
|
412 |
if (capStyle == CapRound) {
|
413 |
poly[0] = coordPtr[0] - radius;
|
414 |
poly[1] = coordPtr[1] - radius;
|
415 |
poly[2] = coordPtr[0] + radius;
|
416 |
poly[3] = coordPtr[1] + radius;
|
417 |
if (TkOvalToArea(poly, rectPtr) != inside) {
|
418 |
return 0;
|
419 |
}
|
420 |
}
|
421 |
|
422 |
return inside;
|
423 |
}
|
424 |
|
425 |
/*
|
426 |
*--------------------------------------------------------------
|
427 |
*
|
428 |
* TkPolygonToPoint --
|
429 |
*
|
430 |
* Compute the distance from a point to a polygon.
|
431 |
*
|
432 |
* Results:
|
433 |
* The return value is 0.0 if the point referred to by
|
434 |
* pointPtr is within the polygon referred to by polyPtr
|
435 |
* and numPoints. Otherwise the return value is the
|
436 |
* distance of the point from the polygon.
|
437 |
*
|
438 |
* Side effects:
|
439 |
* None.
|
440 |
*
|
441 |
*--------------------------------------------------------------
|
442 |
*/
|
443 |
|
444 |
double
|
445 |
TkPolygonToPoint(polyPtr, numPoints, pointPtr)
|
446 |
double *polyPtr; /* Points to an array coordinates for
|
447 |
* closed polygon: x0, y0, x1, y1, ...
|
448 |
* The polygon may be self-intersecting. */
|
449 |
int numPoints; /* Total number of points at *polyPtr. */
|
450 |
double *pointPtr; /* Points to coords for point. */
|
451 |
{
|
452 |
double bestDist; /* Closest distance between point and
|
453 |
* any edge in polygon. */
|
454 |
int intersections; /* Number of edges in the polygon that
|
455 |
* intersect a ray extending vertically
|
456 |
* upwards from the point to infinity. */
|
457 |
int count;
|
458 |
register double *pPtr;
|
459 |
|
460 |
/*
|
461 |
* Iterate through all of the edges in the polygon, updating
|
462 |
* bestDist and intersections.
|
463 |
*
|
464 |
* TRICKY POINT: when computing intersections, include left
|
465 |
* x-coordinate of line within its range, but not y-coordinate.
|
466 |
* Otherwise if the point lies exactly below a vertex we'll
|
467 |
* count it as two intersections.
|
468 |
*/
|
469 |
|
470 |
bestDist = 1.0e36;
|
471 |
intersections = 0;
|
472 |
|
473 |
for (count = numPoints, pPtr = polyPtr; count > 1; count--, pPtr += 2) {
|
474 |
double x, y, dist;
|
475 |
|
476 |
/*
|
477 |
* Compute the point on the current edge closest to the point
|
478 |
* and update the intersection count. This must be done
|
479 |
* separately for vertical edges, horizontal edges, and
|
480 |
* other edges.
|
481 |
*/
|
482 |
|
483 |
if (pPtr[2] == pPtr[0]) {
|
484 |
|
485 |
/*
|
486 |
* Vertical edge.
|
487 |
*/
|
488 |
|
489 |
x = pPtr[0];
|
490 |
if (pPtr[1] >= pPtr[3]) {
|
491 |
y = MIN(pPtr[1], pointPtr[1]);
|
492 |
y = MAX(y, pPtr[3]);
|
493 |
} else {
|
494 |
y = MIN(pPtr[3], pointPtr[1]);
|
495 |
y = MAX(y, pPtr[1]);
|
496 |
}
|
497 |
} else if (pPtr[3] == pPtr[1]) {
|
498 |
|
499 |
/*
|
500 |
* Horizontal edge.
|
501 |
*/
|
502 |
|
503 |
y = pPtr[1];
|
504 |
if (pPtr[0] >= pPtr[2]) {
|
505 |
x = MIN(pPtr[0], pointPtr[0]);
|
506 |
x = MAX(x, pPtr[2]);
|
507 |
if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[0])
|
508 |
&& (pointPtr[0] >= pPtr[2])) {
|
509 |
intersections++;
|
510 |
}
|
511 |
} else {
|
512 |
x = MIN(pPtr[2], pointPtr[0]);
|
513 |
x = MAX(x, pPtr[0]);
|
514 |
if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[2])
|
515 |
&& (pointPtr[0] >= pPtr[0])) {
|
516 |
intersections++;
|
517 |
}
|
518 |
}
|
519 |
} else {
|
520 |
double m1, b1, m2, b2;
|
521 |
int lower; /* Non-zero means point below line. */
|
522 |
|
523 |
/*
|
524 |
* The edge is neither horizontal nor vertical. Convert the
|
525 |
* edge to a line equation of the form y = m1*x + b1. Then
|
526 |
* compute a line perpendicular to this edge but passing
|
527 |
* through the point, also in the form y = m2*x + b2.
|
528 |
*/
|
529 |
|
530 |
m1 = (pPtr[3] - pPtr[1])/(pPtr[2] - pPtr[0]);
|
531 |
b1 = pPtr[1] - m1*pPtr[0];
|
532 |
m2 = -1.0/m1;
|
533 |
b2 = pointPtr[1] - m2*pointPtr[0];
|
534 |
x = (b2 - b1)/(m1 - m2);
|
535 |
y = m1*x + b1;
|
536 |
if (pPtr[0] > pPtr[2]) {
|
537 |
if (x > pPtr[0]) {
|
538 |
x = pPtr[0];
|
539 |
y = pPtr[1];
|
540 |
} else if (x < pPtr[2]) {
|
541 |
x = pPtr[2];
|
542 |
y = pPtr[3];
|
543 |
}
|
544 |
} else {
|
545 |
if (x > pPtr[2]) {
|
546 |
x = pPtr[2];
|
547 |
y = pPtr[3];
|
548 |
} else if (x < pPtr[0]) {
|
549 |
x = pPtr[0];
|
550 |
y = pPtr[1];
|
551 |
}
|
552 |
}
|
553 |
lower = (m1*pointPtr[0] + b1) > pointPtr[1];
|
554 |
if (lower && (pointPtr[0] >= MIN(pPtr[0], pPtr[2]))
|
555 |
&& (pointPtr[0] < MAX(pPtr[0], pPtr[2]))) {
|
556 |
intersections++;
|
557 |
}
|
558 |
}
|
559 |
|
560 |
/*
|
561 |
* Compute the distance to the closest point, and see if that
|
562 |
* is the best distance seen so far.
|
563 |
*/
|
564 |
|
565 |
dist = hypot(pointPtr[0] - x, pointPtr[1] - y);
|
566 |
if (dist < bestDist) {
|
567 |
bestDist = dist;
|
568 |
}
|
569 |
}
|
570 |
|
571 |
/*
|
572 |
* We've processed all of the points. If the number of intersections
|
573 |
* is odd, the point is inside the polygon.
|
574 |
*/
|
575 |
|
576 |
if (intersections & 0x1) {
|
577 |
return 0.0;
|
578 |
}
|
579 |
return bestDist;
|
580 |
}
|
581 |
|
582 |
/*
|
583 |
*--------------------------------------------------------------
|
584 |
*
|
585 |
* TkPolygonToArea --
|
586 |
*
|
587 |
* Determine whether a polygon lies entirely inside, entirely
|
588 |
* outside, or overlapping a given rectangular area.
|
589 |
*
|
590 |
* Results:
|
591 |
* -1 is returned if the polygon given by polyPtr and numPoints
|
592 |
* is entirely outside the rectangle given by rectPtr. 0 is
|
593 |
* returned if the polygon overlaps the rectangle, and 1 is
|
594 |
* returned if the polygon is entirely inside the rectangle.
|
595 |
*
|
596 |
* Side effects:
|
597 |
* None.
|
598 |
*
|
599 |
*--------------------------------------------------------------
|
600 |
*/
|
601 |
|
602 |
int
|
603 |
TkPolygonToArea(polyPtr, numPoints, rectPtr)
|
604 |
double *polyPtr; /* Points to an array coordinates for
|
605 |
* closed polygon: x0, y0, x1, y1, ...
|
606 |
* The polygon may be self-intersecting. */
|
607 |
int numPoints; /* Total number of points at *polyPtr. */
|
608 |
register double *rectPtr; /* Points to coords for rectangle, in the
|
609 |
* order x1, y1, x2, y2. X1 and y1 must
|
610 |
* be lower-left corner. */
|
611 |
{
|
612 |
int state; /* State of all edges seen so far (-1 means
|
613 |
* outside, 1 means inside, won't ever be
|
614 |
* 0). */
|
615 |
int count;
|
616 |
register double *pPtr;
|
617 |
|
618 |
/*
|
619 |
* Iterate over all of the edges of the polygon and test them
|
620 |
* against the rectangle. Can quit as soon as the state becomes
|
621 |
* "intersecting".
|
622 |
*/
|
623 |
|
624 |
state = TkLineToArea(polyPtr, polyPtr+2, rectPtr);
|
625 |
if (state == 0) {
|
626 |
return 0;
|
627 |
}
|
628 |
for (pPtr = polyPtr+2, count = numPoints-1; count >= 2;
|
629 |
pPtr += 2, count--) {
|
630 |
if (TkLineToArea(pPtr, pPtr+2, rectPtr) != state) {
|
631 |
return 0;
|
632 |
}
|
633 |
}
|
634 |
|
635 |
/*
|
636 |
* If all of the edges were inside the rectangle we're done.
|
637 |
* If all of the edges were outside, then the rectangle could
|
638 |
* still intersect the polygon (if it's entirely enclosed).
|
639 |
* Call TkPolygonToPoint to figure this out.
|
640 |
*/
|
641 |
|
642 |
if (state == 1) {
|
643 |
return 1;
|
644 |
}
|
645 |
if (TkPolygonToPoint(polyPtr, numPoints, rectPtr) == 0.0) {
|
646 |
return 0;
|
647 |
}
|
648 |
return -1;
|
649 |
}
|
650 |
|
651 |
/*
|
652 |
*--------------------------------------------------------------
|
653 |
*
|
654 |
* TkOvalToPoint --
|
655 |
*
|
656 |
* Computes the distance from a given point to a given
|
657 |
* oval, in canvas units.
|
658 |
*
|
659 |
* Results:
|
660 |
* The return value is 0 if the point given by *pointPtr is
|
661 |
* inside the oval. If the point isn't inside the
|
662 |
* oval then the return value is approximately the distance
|
663 |
* from the point to the oval. If the oval is filled, then
|
664 |
* anywhere in the interior is considered "inside"; if
|
665 |
* the oval isn't filled, then "inside" means only the area
|
666 |
* occupied by the outline.
|
667 |
*
|
668 |
* Side effects:
|
669 |
* None.
|
670 |
*
|
671 |
*--------------------------------------------------------------
|
672 |
*/
|
673 |
|
674 |
/* ARGSUSED */
|
675 |
double
|
676 |
TkOvalToPoint(ovalPtr, width, filled, pointPtr)
|
677 |
double ovalPtr[4]; /* Pointer to array of four coordinates
|
678 |
* (x1, y1, x2, y2) defining oval's bounding
|
679 |
* box. */
|
680 |
double width; /* Width of outline for oval. */
|
681 |
int filled; /* Non-zero means oval should be treated as
|
682 |
* filled; zero means only consider outline. */
|
683 |
double pointPtr[2]; /* Coordinates of point. */
|
684 |
{
|
685 |
double xDelta, yDelta, scaledDistance, distToOutline, distToCenter;
|
686 |
double xDiam, yDiam;
|
687 |
|
688 |
/*
|
689 |
* Compute the distance between the center of the oval and the
|
690 |
* point in question, using a coordinate system where the oval
|
691 |
* has been transformed to a circle with unit radius.
|
692 |
*/
|
693 |
|
694 |
xDelta = (pointPtr[0] - (ovalPtr[0] + ovalPtr[2])/2.0);
|
695 |
yDelta = (pointPtr[1] - (ovalPtr[1] + ovalPtr[3])/2.0);
|
696 |
distToCenter = hypot(xDelta, yDelta);
|
697 |
scaledDistance = hypot(xDelta / ((ovalPtr[2] + width - ovalPtr[0])/2.0),
|
698 |
yDelta / ((ovalPtr[3] + width - ovalPtr[1])/2.0));
|
699 |
|
700 |
|
701 |
/*
|
702 |
* If the scaled distance is greater than 1 then it means no
|
703 |
* hit. Compute the distance from the point to the edge of
|
704 |
* the circle, then scale this distance back to the original
|
705 |
* coordinate system.
|
706 |
*
|
707 |
* Note: this distance isn't completely accurate. It's only
|
708 |
* an approximation, and it can overestimate the correct
|
709 |
* distance when the oval is eccentric.
|
710 |
*/
|
711 |
|
712 |
if (scaledDistance > 1.0) {
|
713 |
return (distToCenter/scaledDistance) * (scaledDistance - 1.0);
|
714 |
}
|
715 |
|
716 |
/*
|
717 |
* Scaled distance less than 1 means the point is inside the
|
718 |
* outer edge of the oval. If this is a filled oval, then we
|
719 |
* have a hit. Otherwise, do the same computation as above
|
720 |
* (scale back to original coordinate system), but also check
|
721 |
* to see if the point is within the width of the outline.
|
722 |
*/
|
723 |
|
724 |
if (filled) {
|
725 |
return 0.0;
|
726 |
}
|
727 |
if (scaledDistance > 1E-10) {
|
728 |
distToOutline = (distToCenter/scaledDistance) * (1.0 - scaledDistance)
|
729 |
- width;
|
730 |
} else {
|
731 |
/*
|
732 |
* Avoid dividing by a very small number (it could cause an
|
733 |
* arithmetic overflow). This problem occurs if the point is
|
734 |
* very close to the center of the oval.
|
735 |
*/
|
736 |
|
737 |
xDiam = ovalPtr[2] - ovalPtr[0];
|
738 |
yDiam = ovalPtr[3] - ovalPtr[1];
|
739 |
if (xDiam < yDiam) {
|
740 |
distToOutline = (xDiam - width)/2;
|
741 |
} else {
|
742 |
distToOutline = (yDiam - width)/2;
|
743 |
}
|
744 |
}
|
745 |
|
746 |
if (distToOutline < 0.0) {
|
747 |
return 0.0;
|
748 |
}
|
749 |
return distToOutline;
|
750 |
}
|
751 |
|
752 |
/*
|
753 |
*--------------------------------------------------------------
|
754 |
*
|
755 |
* TkOvalToArea --
|
756 |
*
|
757 |
* Determine whether an oval lies entirely inside, entirely
|
758 |
* outside, or overlapping a given rectangular area.
|
759 |
*
|
760 |
* Results:
|
761 |
* -1 is returned if the oval described by ovalPtr is entirely
|
762 |
* outside the rectangle given by rectPtr. 0 is returned if the
|
763 |
* oval overlaps the rectangle, and 1 is returned if the oval
|
764 |
* is entirely inside the rectangle.
|
765 |
*
|
766 |
* Side effects:
|
767 |
* None.
|
768 |
*
|
769 |
*--------------------------------------------------------------
|
770 |
*/
|
771 |
|
772 |
int
|
773 |
TkOvalToArea(ovalPtr, rectPtr)
|
774 |
register double *ovalPtr; /* Points to coordinates definining the
|
775 |
* bounding rectangle for the oval: x1, y1,
|
776 |
* x2, y2. X1 must be less than x2 and y1
|
777 |
* less than y2. */
|
778 |
register double *rectPtr; /* Points to coords for rectangle, in the
|
779 |
* order x1, y1, x2, y2. X1 and y1 must
|
780 |
* be lower-left corner. */
|
781 |
{
|
782 |
double centerX, centerY, radX, radY, deltaX, deltaY;
|
783 |
|
784 |
/*
|
785 |
* First, see if oval is entirely inside rectangle or entirely
|
786 |
* outside rectangle.
|
787 |
*/
|
788 |
|
789 |
if ((rectPtr[0] <= ovalPtr[0]) && (rectPtr[2] >= ovalPtr[2])
|
790 |
&& (rectPtr[1] <= ovalPtr[1]) && (rectPtr[3] >= ovalPtr[3])) {
|
791 |
return 1;
|
792 |
}
|
793 |
if ((rectPtr[2] < ovalPtr[0]) || (rectPtr[0] > ovalPtr[2])
|
794 |
|| (rectPtr[3] < ovalPtr[1]) || (rectPtr[1] > ovalPtr[3])) {
|
795 |
return -1;
|
796 |
}
|
797 |
|
798 |
/*
|
799 |
* Next, go through the rectangle side by side. For each side
|
800 |
* of the rectangle, find the point on the side that is closest
|
801 |
* to the oval's center, and see if that point is inside the
|
802 |
* oval. If at least one such point is inside the oval, then
|
803 |
* the rectangle intersects the oval.
|
804 |
*/
|
805 |
|
806 |
centerX = (ovalPtr[0] + ovalPtr[2])/2;
|
807 |
centerY = (ovalPtr[1] + ovalPtr[3])/2;
|
808 |
radX = (ovalPtr[2] - ovalPtr[0])/2;
|
809 |
radY = (ovalPtr[3] - ovalPtr[1])/2;
|
810 |
|
811 |
deltaY = rectPtr[1] - centerY;
|
812 |
if (deltaY < 0.0) {
|
813 |
deltaY = centerY - rectPtr[3];
|
814 |
if (deltaY < 0.0) {
|
815 |
deltaY = 0;
|
816 |
}
|
817 |
}
|
818 |
deltaY /= radY;
|
819 |
deltaY *= deltaY;
|
820 |
|
821 |
/*
|
822 |
* Left side:
|
823 |
*/
|
824 |
|
825 |
deltaX = (rectPtr[0] - centerX)/radX;
|
826 |
deltaX *= deltaX;
|
827 |
if ((deltaX + deltaY) <= 1.0) {
|
828 |
return 0;
|
829 |
}
|
830 |
|
831 |
/*
|
832 |
* Right side:
|
833 |
*/
|
834 |
|
835 |
deltaX = (rectPtr[2] - centerX)/radX;
|
836 |
deltaX *= deltaX;
|
837 |
if ((deltaX + deltaY) <= 1.0) {
|
838 |
return 0;
|
839 |
}
|
840 |
|
841 |
deltaX = rectPtr[0] - centerX;
|
842 |
if (deltaX < 0.0) {
|
843 |
deltaX = centerX - rectPtr[2];
|
844 |
if (deltaX < 0.0) {
|
845 |
deltaX = 0;
|
846 |
}
|
847 |
}
|
848 |
deltaX /= radX;
|
849 |
deltaX *= deltaX;
|
850 |
|
851 |
/*
|
852 |
* Bottom side:
|
853 |
*/
|
854 |
|
855 |
deltaY = (rectPtr[1] - centerY)/radY;
|
856 |
deltaY *= deltaY;
|
857 |
if ((deltaX + deltaY) < 1.0) {
|
858 |
return 0;
|
859 |
}
|
860 |
|
861 |
/*
|
862 |
* Top side:
|
863 |
*/
|
864 |
|
865 |
deltaY = (rectPtr[3] - centerY)/radY;
|
866 |
deltaY *= deltaY;
|
867 |
if ((deltaX + deltaY) < 1.0) {
|
868 |
return 0;
|
869 |
}
|
870 |
|
871 |
return -1;
|
872 |
}
|
873 |
|
874 |
/*
|
875 |
*--------------------------------------------------------------
|
876 |
*
|
877 |
* TkIncludePoint --
|
878 |
*
|
879 |
* Given a point and a generic canvas item header, expand
|
880 |
* the item's bounding box if needed to include the point.
|
881 |
*
|
882 |
* Results:
|
883 |
* None.
|
884 |
*
|
885 |
* Side effects:
|
886 |
* The boudn.
|
887 |
*
|
888 |
*--------------------------------------------------------------
|
889 |
*/
|
890 |
|
891 |
/* ARGSUSED */
|
892 |
void
|
893 |
TkIncludePoint(itemPtr, pointPtr)
|
894 |
register Tk_Item *itemPtr; /* Item whose bounding box is
|
895 |
* being calculated. */
|
896 |
double *pointPtr; /* Address of two doubles giving
|
897 |
* x and y coordinates of point. */
|
898 |
{
|
899 |
int tmp;
|
900 |
|
901 |
tmp = (int) (pointPtr[0] + 0.5);
|
902 |
if (tmp < itemPtr->x1) {
|
903 |
itemPtr->x1 = tmp;
|
904 |
}
|
905 |
if (tmp > itemPtr->x2) {
|
906 |
itemPtr->x2 = tmp;
|
907 |
}
|
908 |
tmp = (int) (pointPtr[1] + 0.5);
|
909 |
if (tmp < itemPtr->y1) {
|
910 |
itemPtr->y1 = tmp;
|
911 |
}
|
912 |
if (tmp > itemPtr->y2) {
|
913 |
itemPtr->y2 = tmp;
|
914 |
}
|
915 |
}
|
916 |
|
917 |
/*
|
918 |
*--------------------------------------------------------------
|
919 |
*
|
920 |
* TkBezierScreenPoints --
|
921 |
*
|
922 |
* Given four control points, create a larger set of XPoints
|
923 |
* for a Bezier spline based on the points.
|
924 |
*
|
925 |
* Results:
|
926 |
* The array at *xPointPtr gets filled in with numSteps XPoints
|
927 |
* corresponding to the Bezier spline defined by the four
|
928 |
* control points. Note: no output point is generated for the
|
929 |
* first input point, but an output point *is* generated for
|
930 |
* the last input point.
|
931 |
*
|
932 |
* Side effects:
|
933 |
* None.
|
934 |
*
|
935 |
*--------------------------------------------------------------
|
936 |
*/
|
937 |
|
938 |
void
|
939 |
TkBezierScreenPoints(canvas, control, numSteps, xPointPtr)
|
940 |
Tk_Canvas canvas; /* Canvas in which curve is to be
|
941 |
* drawn. */
|
942 |
double control[]; /* Array of coordinates for four
|
943 |
* control points: x0, y0, x1, y1,
|
944 |
* ... x3 y3. */
|
945 |
int numSteps; /* Number of curve points to
|
946 |
* generate. */
|
947 |
register XPoint *xPointPtr; /* Where to put new points. */
|
948 |
{
|
949 |
int i;
|
950 |
double u, u2, u3, t, t2, t3;
|
951 |
|
952 |
for (i = 1; i <= numSteps; i++, xPointPtr++) {
|
953 |
t = ((double) i)/((double) numSteps);
|
954 |
t2 = t*t;
|
955 |
t3 = t2*t;
|
956 |
u = 1.0 - t;
|
957 |
u2 = u*u;
|
958 |
u3 = u2*u;
|
959 |
Tk_CanvasDrawableCoords(canvas,
|
960 |
(control[0]*u3 + 3.0 * (control[2]*t*u2 + control[4]*t2*u)
|
961 |
+ control[6]*t3),
|
962 |
(control[1]*u3 + 3.0 * (control[3]*t*u2 + control[5]*t2*u)
|
963 |
+ control[7]*t3),
|
964 |
&xPointPtr->x, &xPointPtr->y);
|
965 |
}
|
966 |
}
|
967 |
|
968 |
/*
|
969 |
*--------------------------------------------------------------
|
970 |
*
|
971 |
* TkBezierPoints --
|
972 |
*
|
973 |
* Given four control points, create a larger set of points
|
974 |
* for a Bezier spline based on the points.
|
975 |
*
|
976 |
* Results:
|
977 |
* The array at *coordPtr gets filled in with 2*numSteps
|
978 |
* coordinates, which correspond to the Bezier spline defined
|
979 |
* by the four control points. Note: no output point is
|
980 |
* generated for the first input point, but an output point
|
981 |
* *is* generated for the last input point.
|
982 |
*
|
983 |
* Side effects:
|
984 |
* None.
|
985 |
*
|
986 |
*--------------------------------------------------------------
|
987 |
*/
|
988 |
|
989 |
void
|
990 |
TkBezierPoints(control, numSteps, coordPtr)
|
991 |
double control[]; /* Array of coordinates for four
|
992 |
* control points: x0, y0, x1, y1,
|
993 |
* ... x3 y3. */
|
994 |
int numSteps; /* Number of curve points to
|
995 |
* generate. */
|
996 |
register double *coordPtr; /* Where to put new points. */
|
997 |
{
|
998 |
int i;
|
999 |
double u, u2, u3, t, t2, t3;
|
1000 |
|
1001 |
for (i = 1; i <= numSteps; i++, coordPtr += 2) {
|
1002 |
t = ((double) i)/((double) numSteps);
|
1003 |
t2 = t*t;
|
1004 |
t3 = t2*t;
|
1005 |
u = 1.0 - t;
|
1006 |
u2 = u*u;
|
1007 |
u3 = u2*u;
|
1008 |
coordPtr[0] = control[0]*u3
|
1009 |
+ 3.0 * (control[2]*t*u2 + control[4]*t2*u) + control[6]*t3;
|
1010 |
coordPtr[1] = control[1]*u3
|
1011 |
+ 3.0 * (control[3]*t*u2 + control[5]*t2*u) + control[7]*t3;
|
1012 |
}
|
1013 |
}
|
1014 |
|
1015 |
/*
|
1016 |
*--------------------------------------------------------------
|
1017 |
*
|
1018 |
* TkMakeBezierCurve --
|
1019 |
*
|
1020 |
* Given a set of points, create a new set of points that fit
|
1021 |
* parabolic splines to the line segments connecting the original
|
1022 |
* points. Produces output points in either of two forms.
|
1023 |
*
|
1024 |
* Note: in spite of this procedure's name, it does *not* generate
|
1025 |
* Bezier curves. Since only three control points are used for
|
1026 |
* each curve segment, not four, the curves are actually just
|
1027 |
* parabolic.
|
1028 |
*
|
1029 |
* Results:
|
1030 |
* Either or both of the xPoints or dblPoints arrays are filled
|
1031 |
* in. The return value is the number of points placed in the
|
1032 |
* arrays. Note: if the first and last points are the same, then
|
1033 |
* a closed curve is generated.
|
1034 |
*
|
1035 |
* Side effects:
|
1036 |
* None.
|
1037 |
*
|
1038 |
*--------------------------------------------------------------
|
1039 |
*/
|
1040 |
|
1041 |
int
|
1042 |
TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints)
|
1043 |
Tk_Canvas canvas; /* Canvas in which curve is to be
|
1044 |
* drawn. */
|
1045 |
double *pointPtr; /* Array of input coordinates: x0,
|
1046 |
* y0, x1, y1, etc.. */
|
1047 |
int numPoints; /* Number of points at pointPtr. */
|
1048 |
int numSteps; /* Number of steps to use for each
|
1049 |
* spline segments (determines
|
1050 |
* smoothness of curve). */
|
1051 |
XPoint xPoints[]; /* Array of XPoints to fill in (e.g.
|
1052 |
* for display. NULL means don't
|
1053 |
* fill in any XPoints. */
|
1054 |
double dblPoints[]; /* Array of points to fill in as
|
1055 |
* doubles, in the form x0, y0,
|
1056 |
* x1, y1, .... NULL means don't
|
1057 |
* fill in anything in this form.
|
1058 |
* Caller must make sure that this
|
1059 |
* array has enough space. */
|
1060 |
{
|
1061 |
int closed, outputPoints, i;
|
1062 |
int numCoords = numPoints*2;
|
1063 |
double control[8];
|
1064 |
|
1065 |
/*
|
1066 |
* If the curve is a closed one then generate a special spline
|
1067 |
* that spans the last points and the first ones. Otherwise
|
1068 |
* just put the first point into the output.
|
1069 |
*/
|
1070 |
|
1071 |
if (!pointPtr) {
|
1072 |
/* Of pointPtr == NULL, this function returns an upper limit.
|
1073 |
* of the array size to store the coordinates. This can be
|
1074 |
* used to allocate storage, before the actual coordinates
|
1075 |
* are calculated. */
|
1076 |
return 1 + numPoints * numSteps;
|
1077 |
}
|
1078 |
|
1079 |
outputPoints = 0;
|
1080 |
if ((pointPtr[0] == pointPtr[numCoords-2])
|
1081 |
&& (pointPtr[1] == pointPtr[numCoords-1])) {
|
1082 |
closed = 1;
|
1083 |
control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
|
1084 |
control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
|
1085 |
control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
|
1086 |
control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
|
1087 |
control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
|
1088 |
control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
|
1089 |
control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
|
1090 |
control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
|
1091 |
if (xPoints != NULL) {
|
1092 |
Tk_CanvasDrawableCoords(canvas, control[0], control[1],
|
1093 |
&xPoints->x, &xPoints->y);
|
1094 |
TkBezierScreenPoints(canvas, control, numSteps, xPoints+1);
|
1095 |
xPoints += numSteps+1;
|
1096 |
}
|
1097 |
if (dblPoints != NULL) {
|
1098 |
dblPoints[0] = control[0];
|
1099 |
dblPoints[1] = control[1];
|
1100 |
TkBezierPoints(control, numSteps, dblPoints+2);
|
1101 |
dblPoints += 2*(numSteps+1);
|
1102 |
}
|
1103 |
outputPoints += numSteps+1;
|
1104 |
} else {
|
1105 |
closed = 0;
|
1106 |
if (xPoints != NULL) {
|
1107 |
Tk_CanvasDrawableCoords(canvas, pointPtr[0], pointPtr[1],
|
1108 |
&xPoints->x, &xPoints->y);
|
1109 |
xPoints += 1;
|
1110 |
}
|
1111 |
if (dblPoints != NULL) {
|
1112 |
dblPoints[0] = pointPtr[0];
|
1113 |
dblPoints[1] = pointPtr[1];
|
1114 |
dblPoints += 2;
|
1115 |
}
|
1116 |
outputPoints += 1;
|
1117 |
}
|
1118 |
|
1119 |
for (i = 2; i < numPoints; i++, pointPtr += 2) {
|
1120 |
/*
|
1121 |
* Set up the first two control points. This is done
|
1122 |
* differently for the first spline of an open curve
|
1123 |
* than for other cases.
|
1124 |
*/
|
1125 |
|
1126 |
if ((i == 2) && !closed) {
|
1127 |
control[0] = pointPtr[0];
|
1128 |
control[1] = pointPtr[1];
|
1129 |
control[2] = 0.333*pointPtr[0] + 0.667*pointPtr[2];
|
1130 |
control[3] = 0.333*pointPtr[1] + 0.667*pointPtr[3];
|
1131 |
} else {
|
1132 |
control[0] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
|
1133 |
control[1] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
|
1134 |
control[2] = 0.167*pointPtr[0] + 0.833*pointPtr[2];
|
1135 |
control[3] = 0.167*pointPtr[1] + 0.833*pointPtr[3];
|
1136 |
}
|
1137 |
|
1138 |
/*
|
1139 |
* Set up the last two control points. This is done
|
1140 |
* differently for the last spline of an open curve
|
1141 |
* than for other cases.
|
1142 |
*/
|
1143 |
|
1144 |
if ((i == (numPoints-1)) && !closed) {
|
1145 |
control[4] = .667*pointPtr[2] + .333*pointPtr[4];
|
1146 |
control[5] = .667*pointPtr[3] + .333*pointPtr[5];
|
1147 |
control[6] = pointPtr[4];
|
1148 |
control[7] = pointPtr[5];
|
1149 |
} else {
|
1150 |
control[4] = .833*pointPtr[2] + .167*pointPtr[4];
|
1151 |
control[5] = .833*pointPtr[3] + .167*pointPtr[5];
|
1152 |
control[6] = 0.5*pointPtr[2] + 0.5*pointPtr[4];
|
1153 |
control[7] = 0.5*pointPtr[3] + 0.5*pointPtr[5];
|
1154 |
}
|
1155 |
|
1156 |
/*
|
1157 |
* If the first two points coincide, or if the last
|
1158 |
* two points coincide, then generate a single
|
1159 |
* straight-line segment by outputting the last control
|
1160 |
* point.
|
1161 |
*/
|
1162 |
|
1163 |
if (((pointPtr[0] == pointPtr[2]) && (pointPtr[1] == pointPtr[3]))
|
1164 |
|| ((pointPtr[2] == pointPtr[4])
|
1165 |
&& (pointPtr[3] == pointPtr[5]))) {
|
1166 |
if (xPoints != NULL) {
|
1167 |
Tk_CanvasDrawableCoords(canvas, control[6], control[7],
|
1168 |
&xPoints[0].x, &xPoints[0].y);
|
1169 |
xPoints++;
|
1170 |
}
|
1171 |
if (dblPoints != NULL) {
|
1172 |
dblPoints[0] = control[6];
|
1173 |
dblPoints[1] = control[7];
|
1174 |
dblPoints += 2;
|
1175 |
}
|
1176 |
outputPoints += 1;
|
1177 |
continue;
|
1178 |
}
|
1179 |
|
1180 |
/*
|
1181 |
* Generate a Bezier spline using the control points.
|
1182 |
*/
|
1183 |
|
1184 |
|
1185 |
if (xPoints != NULL) {
|
1186 |
TkBezierScreenPoints(canvas, control, numSteps, xPoints);
|
1187 |
xPoints += numSteps;
|
1188 |
}
|
1189 |
if (dblPoints != NULL) {
|
1190 |
TkBezierPoints(control, numSteps, dblPoints);
|
1191 |
dblPoints += 2*numSteps;
|
1192 |
}
|
1193 |
outputPoints += numSteps;
|
1194 |
}
|
1195 |
return outputPoints;
|
1196 |
}
|
1197 |
|
1198 |
/*
|
1199 |
*--------------------------------------------------------------
|
1200 |
*
|
1201 |
* TkMakeBezierPostscript --
|
1202 |
*
|
1203 |
* This procedure generates Postscript commands that create
|
1204 |
* a path corresponding to a given Bezier curve.
|
1205 |
*
|
1206 |
* Results:
|
1207 |
* None. Postscript commands to generate the path are appended
|
1208 |
* to the interp's result.
|
1209 |
*
|
1210 |
* Side effects:
|
1211 |
* None.
|
1212 |
*
|
1213 |
*--------------------------------------------------------------
|
1214 |
*/
|
1215 |
|
1216 |
void
|
1217 |
TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints)
|
1218 |
Tcl_Interp *interp; /* Interpreter in whose result the
|
1219 |
* Postscript is to be stored. */
|
1220 |
Tk_Canvas canvas; /* Canvas widget for which the
|
1221 |
* Postscript is being generated. */
|
1222 |
double *pointPtr; /* Array of input coordinates: x0,
|
1223 |
* y0, x1, y1, etc.. */
|
1224 |
int numPoints; /* Number of points at pointPtr. */
|
1225 |
{
|
1226 |
int closed, i;
|
1227 |
int numCoords = numPoints*2;
|
1228 |
double control[8];
|
1229 |
char buffer[200];
|
1230 |
|
1231 |
/*
|
1232 |
* If the curve is a closed one then generate a special spline
|
1233 |
* that spans the last points and the first ones. Otherwise
|
1234 |
* just put the first point into the path.
|
1235 |
*/
|
1236 |
|
1237 |
if ((pointPtr[0] == pointPtr[numCoords-2])
|
1238 |
&& (pointPtr[1] == pointPtr[numCoords-1])) {
|
1239 |
closed = 1;
|
1240 |
control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
|
1241 |
control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
|
1242 |
control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
|
1243 |
control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
|
1244 |
control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
|
1245 |
control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
|
1246 |
control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
|
1247 |
control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
|
1248 |
sprintf(buffer, "%.15g %.15g moveto\n%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
|
1249 |
control[0], Tk_CanvasPsY(canvas, control[1]),
|
1250 |
control[2], Tk_CanvasPsY(canvas, control[3]),
|
1251 |
control[4], Tk_CanvasPsY(canvas, control[5]),
|
1252 |
control[6], Tk_CanvasPsY(canvas, control[7]));
|
1253 |
} else {
|
1254 |
closed = 0;
|
1255 |
control[6] = pointPtr[0];
|
1256 |
control[7] = pointPtr[1];
|
1257 |
sprintf(buffer, "%.15g %.15g moveto\n",
|
1258 |
control[6], Tk_CanvasPsY(canvas, control[7]));
|
1259 |
}
|
1260 |
Tcl_AppendResult(interp, buffer, (char *) NULL);
|
1261 |
|
1262 |
/*
|
1263 |
* Cycle through all the remaining points in the curve, generating
|
1264 |
* a curve section for each vertex in the linear path.
|
1265 |
*/
|
1266 |
|
1267 |
for (i = numPoints-2, pointPtr += 2; i > 0; i--, pointPtr += 2) {
|
1268 |
control[2] = 0.333*control[6] + 0.667*pointPtr[0];
|
1269 |
control[3] = 0.333*control[7] + 0.667*pointPtr[1];
|
1270 |
|
1271 |
/*
|
1272 |
* Set up the last two control points. This is done
|
1273 |
* differently for the last spline of an open curve
|
1274 |
* than for other cases.
|
1275 |
*/
|
1276 |
|
1277 |
if ((i == 1) && !closed) {
|
1278 |
control[6] = pointPtr[2];
|
1279 |
control[7] = pointPtr[3];
|
1280 |
} else {
|
1281 |
control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
|
1282 |
control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
|
1283 |
}
|
1284 |
control[4] = 0.333*control[6] + 0.667*pointPtr[0];
|
1285 |
control[5] = 0.333*control[7] + 0.667*pointPtr[1];
|
1286 |
|
1287 |
sprintf(buffer, "%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
|
1288 |
control[2], Tk_CanvasPsY(canvas, control[3]),
|
1289 |
control[4], Tk_CanvasPsY(canvas, control[5]),
|
1290 |
control[6], Tk_CanvasPsY(canvas, control[7]));
|
1291 |
Tcl_AppendResult(interp, buffer, (char *) NULL);
|
1292 |
}
|
1293 |
}
|
1294 |
|
1295 |
/*
|
1296 |
*--------------------------------------------------------------
|
1297 |
*
|
1298 |
* TkGetMiterPoints --
|
1299 |
*
|
1300 |
* Given three points forming an angle, compute the
|
1301 |
* coordinates of the inside and outside points of
|
1302 |
* the mitered corner formed by a line of a given
|
1303 |
* width at that angle.
|
1304 |
*
|
1305 |
* Results:
|
1306 |
* If the angle formed by the three points is less than
|
1307 |
* 11 degrees then 0 is returned and m1 and m2 aren't
|
1308 |
* modified. Otherwise 1 is returned and the points at
|
1309 |
* m1 and m2 are filled in with the positions of the points
|
1310 |
* of the mitered corner.
|
1311 |
*
|
1312 |
* Side effects:
|
1313 |
* None.
|
1314 |
*
|
1315 |
*--------------------------------------------------------------
|
1316 |
*/
|
1317 |
|
1318 |
int
|
1319 |
TkGetMiterPoints(p1, p2, p3, width, m1, m2)
|
1320 |
double p1[]; /* Points to x- and y-coordinates of point
|
1321 |
* before vertex. */
|
1322 |
double p2[]; /* Points to x- and y-coordinates of vertex
|
1323 |
* for mitered joint. */
|
1324 |
double p3[]; /* Points to x- and y-coordinates of point
|
1325 |
* after vertex. */
|
1326 |
double width; /* Width of line. */
|
1327 |
double m1[]; /* Points to place to put "left" vertex
|
1328 |
* point (see as you face from p1 to p2). */
|
1329 |
double m2[]; /* Points to place to put "right" vertex
|
1330 |
* point. */
|
1331 |
{
|
1332 |
double theta1; /* Angle of segment p2-p1. */
|
1333 |
double theta2; /* Angle of segment p2-p3. */
|
1334 |
double theta; /* Angle between line segments (angle
|
1335 |
* of joint). */
|
1336 |
double theta3; /* Angle that bisects theta1 and
|
1337 |
* theta2 and points to m1. */
|
1338 |
double dist; /* Distance of miter points from p2. */
|
1339 |
double deltaX, deltaY; /* X and y offsets cooresponding to
|
1340 |
* dist (fudge factors for bounding
|
1341 |
* box). */
|
1342 |
double p1x, p1y, p2x, p2y, p3x, p3y;
|
1343 |
static double elevenDegrees = (11.0*2.0*PI)/360.0;
|
1344 |
|
1345 |
/*
|
1346 |
* Round the coordinates to integers to mimic what happens when the
|
1347 |
* line segments are displayed; without this code, the bounding box
|
1348 |
* of a mitered line can be miscomputed greatly.
|
1349 |
*/
|
1350 |
|
1351 |
p1x = floor(p1[0]+0.5);
|
1352 |
p1y = floor(p1[1]+0.5);
|
1353 |
p2x = floor(p2[0]+0.5);
|
1354 |
p2y = floor(p2[1]+0.5);
|
1355 |
p3x = floor(p3[0]+0.5);
|
1356 |
p3y = floor(p3[1]+0.5);
|
1357 |
|
1358 |
if (p2y == p1y) {
|
1359 |
theta1 = (p2x < p1x) ? 0 : PI;
|
1360 |
} else if (p2x == p1x) {
|
1361 |
theta1 = (p2y < p1y) ? PI/2.0 : -PI/2.0;
|
1362 |
} else {
|
1363 |
theta1 = atan2(p1y - p2y, p1x - p2x);
|
1364 |
}
|
1365 |
if (p3y == p2y) {
|
1366 |
theta2 = (p3x > p2x) ? 0 : PI;
|
1367 |
} else if (p3x == p2x) {
|
1368 |
theta2 = (p3y > p2y) ? PI/2.0 : -PI/2.0;
|
1369 |
} else {
|
1370 |
theta2 = atan2(p3y - p2y, p3x - p2x);
|
1371 |
}
|
1372 |
theta = theta1 - theta2;
|
1373 |
if (theta > PI) {
|
1374 |
theta -= 2*PI;
|
1375 |
} else if (theta < -PI) {
|
1376 |
theta += 2*PI;
|
1377 |
}
|
1378 |
if ((theta < elevenDegrees) && (theta > -elevenDegrees)) {
|
1379 |
return 0;
|
1380 |
}
|
1381 |
dist = 0.5*width/sin(0.5*theta);
|
1382 |
if (dist < 0.0) {
|
1383 |
dist = -dist;
|
1384 |
}
|
1385 |
|
1386 |
/*
|
1387 |
* Compute theta3 (make sure that it points to the left when
|
1388 |
* looking from p1 to p2).
|
1389 |
*/
|
1390 |
|
1391 |
theta3 = (theta1 + theta2)/2.0;
|
1392 |
if (sin(theta3 - (theta1 + PI)) < 0.0) {
|
1393 |
theta3 += PI;
|
1394 |
}
|
1395 |
deltaX = dist*cos(theta3);
|
1396 |
m1[0] = p2x + deltaX;
|
1397 |
m2[0] = p2x - deltaX;
|
1398 |
deltaY = dist*sin(theta3);
|
1399 |
m1[1] = p2y + deltaY;
|
1400 |
m2[1] = p2y - deltaY;
|
1401 |
return 1;
|
1402 |
}
|
1403 |
|
1404 |
/*
|
1405 |
*--------------------------------------------------------------
|
1406 |
*
|
1407 |
* TkGetButtPoints --
|
1408 |
*
|
1409 |
* Given two points forming a line segment, compute the
|
1410 |
* coordinates of two endpoints of a rectangle formed by
|
1411 |
* bloating the line segment until it is width units wide.
|
1412 |
*
|
1413 |
* Results:
|
1414 |
* There is no return value. M1 and m2 are filled in to
|
1415 |
* correspond to m1 and m2 in the diagram below:
|
1416 |
*
|
1417 |
* ----------------* m1
|
1418 |
* |
|
1419 |
* p1 *---------------* p2
|
1420 |
* |
|
1421 |
* ----------------* m2
|
1422 |
*
|
1423 |
* M1 and m2 will be W units apart, with p2 centered between
|
1424 |
* them and m1-m2 perpendicular to p1-p2. However, if
|
1425 |
* "project" is true then m1 and m2 will be as follows:
|
1426 |
*
|
1427 |
* -------------------* m1
|
1428 |
* p2 |
|
1429 |
* p1 *---------------* |
|
1430 |
* |
|
1431 |
* -------------------* m2
|
1432 |
*
|
1433 |
* In this case p2 will be width/2 units from the segment m1-m2.
|
1434 |
*
|
1435 |
* Side effects:
|
1436 |
* None.
|
1437 |
*
|
1438 |
*--------------------------------------------------------------
|
1439 |
*/
|
1440 |
|
1441 |
void
|
1442 |
TkGetButtPoints(p1, p2, width, project, m1, m2)
|
1443 |
double p1[]; /* Points to x- and y-coordinates of point
|
1444 |
* before vertex. */
|
1445 |
double p2[]; /* Points to x- and y-coordinates of vertex
|
1446 |
* for mitered joint. */
|
1447 |
double width; /* Width of line. */
|
1448 |
int project; /* Non-zero means project p2 by an additional
|
1449 |
* width/2 before computing m1 and m2. */
|
1450 |
double m1[]; /* Points to place to put "left" result
|
1451 |
* point, as you face from p1 to p2. */
|
1452 |
double m2[]; /* Points to place to put "right" result
|
1453 |
* point. */
|
1454 |
{
|
1455 |
double length; /* Length of p1-p2 segment. */
|
1456 |
double deltaX, deltaY; /* Increments in coords. */
|
1457 |
|
1458 |
width *= 0.5;
|
1459 |
length = hypot(p2[0] - p1[0], p2[1] - p1[1]);
|
1460 |
if (length == 0.0) {
|
1461 |
m1[0] = m2[0] = p2[0];
|
1462 |
m1[1] = m2[1] = p2[1];
|
1463 |
} else {
|
1464 |
deltaX = -width * (p2[1] - p1[1]) / length;
|
1465 |
deltaY = width * (p2[0] - p1[0]) / length;
|
1466 |
m1[0] = p2[0] + deltaX;
|
1467 |
m2[0] = p2[0] - deltaX;
|
1468 |
m1[1] = p2[1] + deltaY;
|
1469 |
m2[1] = p2[1] - deltaY;
|
1470 |
if (project) {
|
1471 |
m1[0] += deltaY;
|
1472 |
m2[0] += deltaY;
|
1473 |
m1[1] -= deltaX;
|
1474 |
m2[1] -= deltaX;
|
1475 |
}
|
1476 |
}
|
1477 |
}
|
1478 |
|
1479 |
|
1480 |
/* $History: tkTrig.c $
|
1481 |
*
|
1482 |
* ***************** Version 1 *****************
|
1483 |
* User: Dtashley Date: 1/02/01 Time: 3:05a
|
1484 |
* Created in $/IjuScripter, IjuConsole/Source/Tk Base
|
1485 |
* Initial check-in.
|
1486 |
*/
|
1487 |
|
1488 |
/* End of TKTRIG.C */ |