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/*
* tkTrig.c --
*
* This file contains a collection of trigonometry utility
* routines that are used by Tk and in particular by the
* canvas code. It also has miscellaneous geometry functions
* used by canvases.
*
* Copyright (c) 1992-1994 The Regents of the University of California.
* Copyright (c) 1994 Sun Microsystems, Inc.
*
* See the file "license.terms" for information on usage and redistribution
* of this file, and for a DISCLAIMER OF ALL WARRANTIES.
*
* SCCS: @(#) tkTrig.c 1.27 97/03/07 11:34:35
*/
#include <stdio.h>
#include "tkInt.h"
#include "tkPort.h"
#include "tkCanvas.h"
#undef MIN
#define MIN(a,b) (((a) < (b)) ? (a) : (b))
#undef MAX
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
#ifndef PI
# define PI 3.14159265358979323846
#endif /* PI */
/*
*--------------------------------------------------------------
*
* TkLineToPoint --
*
* Compute the distance from a point to a finite line segment.
*
* Results:
* The return value is the distance from the line segment
* whose end-points are *end1Ptr and *end2Ptr to the point
* given by *pointPtr.
*
* Side effects:
* None.
*
*--------------------------------------------------------------
*/
double
TkLineToPoint(end1Ptr, end2Ptr, pointPtr)
double end1Ptr[2]; /* Coordinates of first end-point of line. */
double end2Ptr[2]; /* Coordinates of second end-point of line. */
double pointPtr[2]; /* Points to coords for point. */
{
double x, y;
/*
* Compute the point on the line that is closest to the
* point. This must be done separately for vertical edges,
* horizontal edges, and other edges.
*/
if (end1Ptr[0] == end2Ptr[0]) {
/*
* Vertical edge.
*/
x = end1Ptr[0];
if (end1Ptr[1] >= end2Ptr[1]) {
y = MIN(end1Ptr[1], pointPtr[1]);
y = MAX(y, end2Ptr[1]);
} else {
y = MIN(end2Ptr[1], pointPtr[1]);
y = MAX(y, end1Ptr[1]);
}
} else if (end1Ptr[1] == end2Ptr[1]) {
/*
* Horizontal edge.
*/
y = end1Ptr[1];
if (end1Ptr[0] >= end2Ptr[0]) {
x = MIN(end1Ptr[0], pointPtr[0]);
x = MAX(x, end2Ptr[0]);
} else {
x = MIN(end2Ptr[0], pointPtr[0]);
x = MAX(x, end1Ptr[0]);
}
} else {
double m1, b1, m2, b2;
/*
* The edge is neither horizontal nor vertical. Convert the
* edge to a line equation of the form y = m1*x + b1. Then
* compute a line perpendicular to this edge but passing
* through the point, also in the form y = m2*x + b2.
*/
m1 = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]);
b1 = end1Ptr[1] - m1*end1Ptr[0];
m2 = -1.0/m1;
b2 = pointPtr[1] - m2*pointPtr[0];
x = (b2 - b1)/(m1 - m2);
y = m1*x + b1;
if (end1Ptr[0] > end2Ptr[0]) {
if (x > end1Ptr[0]) {
x = end1Ptr[0];
y = end1Ptr[1];
} else if (x < end2Ptr[0]) {
x = end2Ptr[0];
y = end2Ptr[1];
}
} else {
if (x > end2Ptr[0]) {
x = end2Ptr[0];
y = end2Ptr[1];
} else if (x < end1Ptr[0]) {
x = end1Ptr[0];
y = end1Ptr[1];
}
}
}
/*
* Compute the distance to the closest point.
*/
return hypot(pointPtr[0] - x, pointPtr[1] - y);
}
/*
*--------------------------------------------------------------
*
* TkLineToArea --
*
* Determine whether a line lies entirely inside, entirely
* outside, or overlapping a given rectangular area.
*
* Results:
* -1 is returned if the line given by end1Ptr and end2Ptr
* is entirely outside the rectangle given by rectPtr. 0 is
* returned if the polygon overlaps the rectangle, and 1 is
* returned if the polygon is entirely inside the rectangle.
*
* Side effects:
* None.
*
*--------------------------------------------------------------
*/
int
TkLineToArea(end1Ptr, end2Ptr, rectPtr)
double end1Ptr[2]; /* X and y coordinates for one endpoint
* of line. */
double end2Ptr[2]; /* X and y coordinates for other endpoint
* of line. */
double rectPtr[4]; /* Points to coords for rectangle, in the
* order x1, y1, x2, y2. X1 must be no
* larger than x2, and y1 no larger than y2. */
{
int inside1, inside2;
/*
* First check the two points individually to see whether they
* are inside the rectangle or not.
*/
inside1 = (end1Ptr[0] >= rectPtr[0]) && (end1Ptr[0] <= rectPtr[2])
&& (end1Ptr[1] >= rectPtr[1]) && (end1Ptr[1] <= rectPtr[3]);
inside2 = (end2Ptr[0] >= rectPtr[0]) && (end2Ptr[0] <= rectPtr[2])
&& (end2Ptr[1] >= rectPtr[1]) && (end2Ptr[1] <= rectPtr[3]);
if (inside1 != inside2) {
return 0;
}
if (inside1 & inside2) {
return 1;
}
/*
* Both points are outside the rectangle, but still need to check
* for intersections between the line and the rectangle. Horizontal
* and vertical lines are particularly easy, so handle them
* separately.
*/
if (end1Ptr[0] == end2Ptr[0]) {
/*
* Vertical line.
*/
if (((end1Ptr[1] >= rectPtr[1]) ^ (end2Ptr[1] >= rectPtr[1]))
&& (end1Ptr[0] >= rectPtr[0])
&& (end1Ptr[0] <= rectPtr[2])) {
return 0;
}
} else if (end1Ptr[1] == end2Ptr[1]) {
/*
* Horizontal line.
*/
if (((end1Ptr[0] >= rectPtr[0]) ^ (end2Ptr[0] >= rectPtr[0]))
&& (end1Ptr[1] >= rectPtr[1])
&& (end1Ptr[1] <= rectPtr[3])) {
return 0;
}
} else {
double m, x, y, low, high;
/*
* Diagonal line. Compute slope of line and use
* for intersection checks against each of the
* sides of the rectangle: left, right, bottom, top.
*/
m = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]);
if (end1Ptr[0] < end2Ptr[0]) {
low = end1Ptr[0]; high = end2Ptr[0];
} else {
low = end2Ptr[0]; high = end1Ptr[0];
}
/*
* Left edge.
*/
y = end1Ptr[1] + (rectPtr[0] - end1Ptr[0])*m;
if ((rectPtr[0] >= low) && (rectPtr[0] <= high)
&& (y >= rectPtr[1]) && (y <= rectPtr[3])) {
return 0;
}
/*
* Right edge.
*/
y += (rectPtr[2] - rectPtr[0])*m;
if ((y >= rectPtr[1]) && (y <= rectPtr[3])
&& (rectPtr[2] >= low) && (rectPtr[2] <= high)) {
return 0;
}
/*
* Bottom edge.
*/
if (end1Ptr[1] < end2Ptr[1]) {
low = end1Ptr[1]; high = end2Ptr[1];
} else {
low = end2Ptr[1]; high = end1Ptr[1];
}
x = end1Ptr[0] + (rectPtr[1] - end1Ptr[1])/m;
if ((x >= rectPtr[0]) && (x <= rectPtr[2])
&& (rectPtr[1] >= low) && (rectPtr[1] <= high)) {
return 0;
}
/*
* Top edge.
*/
x += (rectPtr[3] - rectPtr[1])/m;
if ((x >= rectPtr[0]) && (x <= rectPtr[2])
&& (rectPtr[3] >= low) && (rectPtr[3] <= high)) {
return 0;
}
}
return -1;
}
/*
*--------------------------------------------------------------
*
* TkThickPolyLineToArea --
*
* This procedure is called to determine whether a connected
* series of line segments lies entirely inside, entirely
* outside, or overlapping a given rectangular area.
*
* Results:
* -1 is returned if the lines are entirely outside the area,
* 0 if they overlap, and 1 if they are entirely inside the
* given area.
*
* Side effects:
* None.
*
*--------------------------------------------------------------
*/
/* ARGSUSED */
int
TkThickPolyLineToArea(coordPtr, numPoints, width, capStyle, joinStyle, rectPtr)
double *coordPtr; /* Points to an array of coordinates for
* the polyline: x0, y0, x1, y1, ... */
int numPoints; /* Total number of points at *coordPtr. */
double width; /* Width of each line segment. */
int capStyle; /* How are end-points of polyline drawn?
* CapRound, CapButt, or CapProjecting. */
int joinStyle; /* How are joints in polyline drawn?
* JoinMiter, JoinRound, or JoinBevel. */
double *rectPtr; /* Rectangular area to check against. */
{
double radius, poly[10];
int count;
int changedMiterToBevel; /* Non-zero means that a mitered corner
* had to be treated as beveled after all
* because the angle was < 11 degrees. */
int inside; /* Tentative guess about what to return,
* based on all points seen so far: one
* means everything seen so far was
* inside the area; -1 means everything
* was outside the area. 0 means overlap
* has been found. */
radius = width/2.0;
inside = -1;
if ((coordPtr[0] >= rectPtr[0]) && (coordPtr[0] <= rectPtr[2])
&& (coordPtr[1] >= rectPtr[1]) && (coordPtr[1] <= rectPtr[3])) {
inside = 1;
}
/*
* Iterate through all of the edges of the line, computing a polygon
* for each edge and testing the area against that polygon. In
* addition, there are additional tests to deal with rounded joints
* and caps.
*/
changedMiterToBevel = 0;
for (count = numPoints; count >= 2; count--, coordPtr += 2) {
/*
* If rounding is done around the first point of the edge
* then test a circular region around the point with the
* area.
*/
if (((capStyle == CapRound) && (count == numPoints))
|| ((joinStyle == JoinRound) && (count != numPoints))) {
poly[0] = coordPtr[0] - radius;
poly[1] = coordPtr[1] - radius;
poly[2] = coordPtr[0] + radius;
poly[3] = coordPtr[1] + radius;
if (TkOvalToArea(poly, rectPtr) != inside) {
return 0;
}
}
/*
* Compute the polygonal shape corresponding to this edge,
* consisting of two points for the first point of the edge
* and two points for the last point of the edge.
*/
if (count == numPoints) {
TkGetButtPoints(coordPtr+2, coordPtr, width,
capStyle == CapProjecting, poly, poly+2);
} else if ((joinStyle == JoinMiter) && !changedMiterToBevel) {
poly[0] = poly[6];
poly[1] = poly[7];
poly[2] = poly[4];
poly[3] = poly[5];
} else {
TkGetButtPoints(coordPtr+2, coordPtr, width, 0, poly, poly+2);
/*
* If the last joint was beveled, then also check a
* polygon comprising the last two points of the previous
* polygon and the first two from this polygon; this checks
* the wedges that fill the beveled joint.
*/
if ((joinStyle == JoinBevel) || changedMiterToBevel) {
poly[8] = poly[0];
poly[9] = poly[1];
if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
return 0;
}
changedMiterToBevel = 0;
}
}
if (count == 2) {
TkGetButtPoints(coordPtr, coordPtr+2, width,
capStyle == CapProjecting, poly+4, poly+6);
} else if (joinStyle == JoinMiter) {
if (TkGetMiterPoints(coordPtr, coordPtr+2, coordPtr+4,
(double) width, poly+4, poly+6) == 0) {
changedMiterToBevel = 1;
TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4,
poly+6);
}
} else {
TkGetButtPoints(coordPtr, coordPtr+2, width, 0, poly+4, poly+6);
}
poly[8] = poly[0];
poly[9] = poly[1];
if (TkPolygonToArea(poly, 5, rectPtr) != inside) {
return 0;
}
}
/*
* If caps are rounded, check the cap around the final point
* of the line.
*/
if (capStyle == CapRound) {
poly[0] = coordPtr[0] - radius;
poly[1] = coordPtr[1] - radius;
poly[2] = coordPtr[0] + radius;
poly[3] = coordPtr[1] + radius;
if (TkOvalToArea(poly, rectPtr) != inside) {
return 0;
}
}
return inside;
}
/*
*--------------------------------------------------------------
*
* TkPolygonToPoint --
*
* Compute the distance from a point to a polygon.
*
* Results:
* The return value is 0.0 if the point referred to by
* pointPtr is within the polygon referred to by polyPtr
* and numPoints. Otherwise the return value is the
* distance of the point from the polygon.
*
* Side effects:
* None.
*
*--------------------------------------------------------------
*/
double
TkPolygonToPoint(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 = (int) (pointPtr[0] + 0.5);
if (tmp < itemPtr->x1) {
itemPtr->x1 = tmp;
}
if (tmp > itemPtr->x2) {
itemPtr->x2 = tmp;
}
tmp = (int) (pointPtr[1] + 0.5);
if (tmp < itemPtr->y1) {
itemPtr->y1 = tmp;
}
if (tmp > itemPtr->y2) {
itemPtr->y2 = tmp;
}
}
/*
*--------------------------------------------------------------
*
* TkBezierScreenPoints --
*
* Given four control points, create a larger set of XPoints
* for a Bezier 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
* parabolic splines to the line segments connecting the original
* points. Produces output points in either of two forms.
*
* Note: in spite of this procedure's name, it does *not* generate
* Bezier curves. Since only three control points are used for
* each curve segment, not four, the curves are actually just
* parabolic.
*
* 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). */
double p1x, p1y, p2x, p2y, p3x, p3y;
static double elevenDegrees = (11.0*2.0*PI)/360.0;
/*
* Round the coordinates to integers to mimic what happens when the
* line segments are displayed; without this code, the bounding box
* of a mitered line can be miscomputed greatly.
*/
p1x = floor(p1[0]+0.5);
p1y = floor(p1[1]+0.5);
p2x = floor(p2[0]+0.5);
p2y = floor(p2[1]+0.5);
p3x = floor(p3[0]+0.5);
p3y = floor(p3[1]+0.5);
if (p2y == p1y) {
theta1 = (p2x < p1x) ? 0 : PI;
} else if (p2x == p1x) {
theta1 = (p2y < p1y) ? PI/2.0 : -PI/2.0;
} else {
theta1 = atan2(p1y - p2y, p1x - p2x);
}
if (p3y == p2y) {
theta2 = (p3x > p2x) ? 0 : PI;
} else if (p3x == p2x) {
theta2 = (p3y > p2y) ? PI/2.0 : -PI/2.0;
} else {
theta2 = atan2(p3y - p2y, p3x - p2x);
}
theta = theta1 - theta2;
if (theta > PI) {
theta -= 2*PI;
} else if (theta < -PI) {
theta += 2*PI;
}
if ((theta < elevenDegrees) && (theta > -elevenDegrees)) {
return 0;
}
dist = 0.5*width/sin(0.5*theta);
if (dist < 0.0) {
dist = -dist;
}
/*
* Compute theta3 (make sure that it points to the left when
* looking from p1 to p2).
*/
theta3 = (theta1 + theta2)/2.0;
if (sin(theta3 - (theta1 + PI)) < 0.0) {
theta3 += PI;
}
deltaX = dist*cos(theta3);
m1[0] = p2x + deltaX;
m2[0] = p2x - deltaX;
deltaY = dist*sin(theta3);
m1[1] = p2y + deltaY;
m2[1] = p2y - deltaY;
return 1;
}
/*
*--------------------------------------------------------------
*
* TkGetButtPoints --
*
* Given two points forming a line segment, compute the
* coordinates of two endpoints of a rectangle formed by
* bloating the line segment until it is width units wide.
*
* Results:
* There is no return value. M1 and m2 are filled in to
* correspond to m1 and m2 in the diagram below:
*
* ----------------* m1
* |
* p1 *---------------* p2
* |
* ----------------* m2
*
* M1 and m2 will be W units apart, with p2 centered between
* them and m1-m2 perpendicular to p1-p2. However, if
* "project" is true then m1 and m2 will be as follows:
*
* -------------------* m1
* p2 |
* p1 *---------------* |
* |
* -------------------* m2
*
* In this case p2 will be width/2 units from the segment m1-m2.
*
* Side effects:
* None.
*
*--------------------------------------------------------------
*/
void
TkGetButtPoints(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;
}
}
}
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