/*
* Copyright (c) 2016 Martin Davis.
*
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* and Eclipse Distribution License v. 1.0 which accompanies this distribution.
* The Eclipse Public License is available at http://www.eclipse.org/legal/epl-v10.html
* and the Eclipse Distribution License is available at
*
* http://www.eclipse.org/org/documents/edl-v10.php.
*/
package org.locationtech.jts.operation.buffer;
import org.locationtech.jts.algorithm.Angle;
import org.locationtech.jts.algorithm.CGAlgorithms;
import org.locationtech.jts.algorithm.HCoordinate;
import org.locationtech.jts.algorithm.LineIntersector;
import org.locationtech.jts.algorithm.NotRepresentableException;
import org.locationtech.jts.algorithm.RobustLineIntersector;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.geom.LineSegment;
import org.locationtech.jts.geom.PrecisionModel;
import org.locationtech.jts.geomgraph.Position;
/**
* Generates segments which form an offset curve.
* Supports all end cap and join options
* provided for buffering.
* This algorithm implements various heuristics to
* produce smoother, simpler curves which are
* still within a reasonable tolerance of the
* true curve.
*
* @author Martin Davis
*
*/
class OffsetSegmentGenerator
{
/**
* Factor which controls how close offset segments can be to
* skip adding a filler or mitre.
*/
private static final double OFFSET_SEGMENT_SEPARATION_FACTOR = 1.0E-3;
/**
* Factor which controls how close curve vertices on inside turns can be to be snapped
*/
private static final double INSIDE_TURN_VERTEX_SNAP_DISTANCE_FACTOR = 1.0E-3;
/**
* Factor which controls how close curve vertices can be to be snapped
*/
private static final double CURVE_VERTEX_SNAP_DISTANCE_FACTOR = 1.0E-6;
/**
* Factor which determines how short closing segs can be for round buffers
*/
private static final int MAX_CLOSING_SEG_LEN_FACTOR = 80;
/**
* the max error of approximation (distance) between a quad segment and the true fillet curve
*/
private double maxCurveSegmentError = 0.0;
/**
* The angle quantum with which to approximate a fillet curve
* (based on the input # of quadrant segments)
*/
private double filletAngleQuantum;
/**
* The Closing Segment Length Factor controls how long
* "closing segments" are. Closing segments are added
* at the middle of inside corners to ensure a smoother
* boundary for the buffer offset curve.
* In some cases (particularly for round joins with default-or-better
* quantization) the closing segments can be made quite short.
* This substantially improves performance (due to fewer intersections being created).
*
* A closingSegFactor of 0 results in lines to the corner vertex
* A closingSegFactor of 1 results in lines halfway to the corner vertex
* A closingSegFactor of 80 results in lines 1/81 of the way to the corner vertex
* (this option is reasonable for the very common default situation of round joins
* and quadrantSegs >= 8)
*/
private int closingSegLengthFactor = 1;
private OffsetSegmentString segList;
private double distance = 0.0;
private PrecisionModel precisionModel;
private BufferParameters bufParams;
private LineIntersector li;
private Coordinate s0, s1, s2;
private LineSegment seg0 = new LineSegment();
private LineSegment seg1 = new LineSegment();
private LineSegment offset0 = new LineSegment();
private LineSegment offset1 = new LineSegment();
private int side = 0;
private boolean hasNarrowConcaveAngle = false;
public OffsetSegmentGenerator(PrecisionModel precisionModel,
BufferParameters bufParams, double distance) {
this.precisionModel = precisionModel;
this.bufParams = bufParams;
// compute intersections in full precision, to provide accuracy
// the points are rounded as they are inserted into the curve line
li = new RobustLineIntersector();
filletAngleQuantum = Math.PI / 2.0 / bufParams.getQuadrantSegments();
/**
* Non-round joins cause issues with short closing segments, so don't use
* them. In any case, non-round joins only really make sense for relatively
* small buffer distances.
*/
if (bufParams.getQuadrantSegments() >= 8
&& bufParams.getJoinStyle() == BufferParameters.JOIN_ROUND)
closingSegLengthFactor = MAX_CLOSING_SEG_LEN_FACTOR;
init(distance);
}
/**
* Tests whether the input has a narrow concave angle
* (relative to the offset distance).
* In this case the generated offset curve will contain self-intersections
* and heuristic closing segments.
* This is expected behaviour in the case of Buffer curves.
* For pure Offset Curves,
* the output needs to be further treated
* before it can be used.
*
* @return true if the input has a narrow concave angle
*/
public boolean hasNarrowConcaveAngle()
{
return hasNarrowConcaveAngle;
}
private void init(double distance)
{
this.distance = distance;
maxCurveSegmentError = distance * (1 - Math.cos(filletAngleQuantum / 2.0));
segList = new OffsetSegmentString();
segList.setPrecisionModel(precisionModel);
/**
* Choose the min vertex separation as a small fraction of the offset distance.
*/
segList.setMinimumVertexDistance(distance * CURVE_VERTEX_SNAP_DISTANCE_FACTOR);
}
public void initSideSegments(Coordinate s1, Coordinate s2, int side)
{
this.s1 = s1;
this.s2 = s2;
this.side = side;
seg1.setCoordinates(s1, s2);
computeOffsetSegment(seg1, side, distance, offset1);
}
public Coordinate[] getCoordinates()
{
Coordinate[] pts = segList.getCoordinates();
return pts;
}
public void closeRing()
{
segList.closeRing();
}
public void addSegments(Coordinate[] pt, boolean isForward)
{
segList.addPts(pt, isForward);
}
public void addFirstSegment()
{
segList.addPt(offset1.p0);
}
/**
* Add last offset point
*/
public void addLastSegment()
{
segList.addPt(offset1.p1);
}
//private static double MAX_CLOSING_SEG_LEN = 3.0;
public void addNextSegment(Coordinate p, boolean addStartPoint)
{
// s0-s1-s2 are the coordinates of the previous segment and the current one
s0 = s1;
s1 = s2;
s2 = p;
seg0.setCoordinates(s0, s1);
computeOffsetSegment(seg0, side, distance, offset0);
seg1.setCoordinates(s1, s2);
computeOffsetSegment(seg1, side, distance, offset1);
// do nothing if points are equal
if (s1.equals(s2)) return;
int orientation = CGAlgorithms.computeOrientation(s0, s1, s2);
boolean outsideTurn =
(orientation == CGAlgorithms.CLOCKWISE && side == Position.LEFT)
|| (orientation == CGAlgorithms.COUNTERCLOCKWISE && side == Position.RIGHT);
if (orientation == 0) { // lines are collinear
addCollinear(addStartPoint);
}
else if (outsideTurn)
{
addOutsideTurn(orientation, addStartPoint);
}
else { // inside turn
addInsideTurn(orientation, addStartPoint);
}
}
private void addCollinear(boolean addStartPoint)
{
/**
* This test could probably be done more efficiently,
* but the situation of exact collinearity should be fairly rare.
*/
li.computeIntersection(s0, s1, s1, s2);
int numInt = li.getIntersectionNum();
/**
* if numInt is < 2, the lines are parallel and in the same direction. In
* this case the point can be ignored, since the offset lines will also be
* parallel.
*/
if (numInt >= 2) {
/**
* segments are collinear but reversing.
* Add an "end-cap" fillet
* all the way around to other direction This case should ONLY happen
* for LineStrings, so the orientation is always CW. (Polygons can never
* have two consecutive segments which are parallel but reversed,
* because that would be a self intersection.
*
*/
if (bufParams.getJoinStyle() == BufferParameters.JOIN_BEVEL
|| bufParams.getJoinStyle() == BufferParameters.JOIN_MITRE) {
if (addStartPoint) segList.addPt(offset0.p1);
segList.addPt(offset1.p0);
}
else {
addFillet(s1, offset0.p1, offset1.p0, CGAlgorithms.CLOCKWISE, distance);
}
}
}
/**
* Adds the offset points for an outside (convex) turn
*
* @param orientation
* @param addStartPoint
*/
private void addOutsideTurn(int orientation, boolean addStartPoint)
{
/**
* Heuristic: If offset endpoints are very close together,
* just use one of them as the corner vertex.
* This avoids problems with computing mitre corners in the case
* where the two segments are almost parallel
* (which is hard to compute a robust intersection for).
*/
if (offset0.p1.distance(offset1.p0) < distance * OFFSET_SEGMENT_SEPARATION_FACTOR) {
segList.addPt(offset0.p1);
return;
}
if (bufParams.getJoinStyle() == BufferParameters.JOIN_MITRE) {
addMitreJoin(s1, offset0, offset1, distance);
}
else if (bufParams.getJoinStyle() == BufferParameters.JOIN_BEVEL){
addBevelJoin(offset0, offset1);
}
else {
// add a circular fillet connecting the endpoints of the offset segments
if (addStartPoint) segList.addPt(offset0.p1);
// TESTING - comment out to produce beveled joins
addFillet(s1, offset0.p1, offset1.p0, orientation, distance);
segList.addPt(offset1.p0);
}
}
/**
* Adds the offset points for an inside (concave) turn.
*
* @param orientation
* @param addStartPoint
*/
private void addInsideTurn(int orientation, boolean addStartPoint) {
/**
* add intersection point of offset segments (if any)
*/
li.computeIntersection(offset0.p0, offset0.p1, offset1.p0, offset1.p1);
if (li.hasIntersection()) {
segList.addPt(li.getIntersection(0));
}
else {
/**
* If no intersection is detected,
* it means the angle is so small and/or the offset so
* large that the offsets segments don't intersect.
* In this case we must
* add a "closing segment" to make sure the buffer curve is continuous,
* fairly smooth (e.g. no sharp reversals in direction)
* and tracks the buffer correctly around the corner. The curve connects
* the endpoints of the segment offsets to points
* which lie toward the centre point of the corner.
* The joining curve will not appear in the final buffer outline, since it
* is completely internal to the buffer polygon.
*
* In complex buffer cases the closing segment may cut across many other
* segments in the generated offset curve. In order to improve the
* performance of the noding, the closing segment should be kept as short as possible.
* (But not too short, since that would defeat its purpose).
* This is the purpose of the closingSegFactor heuristic value.
*/
/**
* The intersection test above is vulnerable to robustness errors; i.e. it
* may be that the offsets should intersect very close to their endpoints,
* but aren't reported as such due to rounding. To handle this situation
* appropriately, we use the following test: If the offset points are very
* close, don't add closing segments but simply use one of the offset
* points
*/
hasNarrowConcaveAngle = true;
//System.out.println("NARROW ANGLE - distance = " + distance);
if (offset0.p1.distance(offset1.p0) < distance
* INSIDE_TURN_VERTEX_SNAP_DISTANCE_FACTOR) {
segList.addPt(offset0.p1);
} else {
// add endpoint of this segment offset
segList.addPt(offset0.p1);
/**
* Add "closing segment" of required length.
*/
if (closingSegLengthFactor > 0) {
Coordinate mid0 = new Coordinate((closingSegLengthFactor * offset0.p1.x + s1.x)/(closingSegLengthFactor + 1),
(closingSegLengthFactor*offset0.p1.y + s1.y)/(closingSegLengthFactor + 1));
segList.addPt(mid0);
Coordinate mid1 = new Coordinate((closingSegLengthFactor*offset1.p0.x + s1.x)/(closingSegLengthFactor + 1),
(closingSegLengthFactor*offset1.p0.y + s1.y)/(closingSegLengthFactor + 1));
segList.addPt(mid1);
}
else {
/**
* This branch is not expected to be used except for testing purposes.
* It is equivalent to the JTS 1.9 logic for closing segments
* (which results in very poor performance for large buffer distances)
*/
segList.addPt(s1);
}
//*/
// add start point of next segment offset
segList.addPt(offset1.p0);
}
}
}
/**
* Compute an offset segment for an input segment on a given side and at a given distance.
* The offset points are computed in full double precision, for accuracy.
*
* @param seg the segment to offset
* @param side the side of the segment ({@link Position}) the offset lies on
* @param distance the offset distance
* @param offset the points computed for the offset segment
*/
private void computeOffsetSegment(LineSegment seg, int side, double distance, LineSegment offset)
{
int sideSign = side == Position.LEFT ? 1 : -1;
double dx = seg.p1.x - seg.p0.x;
double dy = seg.p1.y - seg.p0.y;
double len = Math.sqrt(dx * dx + dy * dy);
// u is the vector that is the length of the offset, in the direction of the segment
double ux = sideSign * distance * dx / len;
double uy = sideSign * distance * dy / len;
offset.p0.x = seg.p0.x - uy;
offset.p0.y = seg.p0.y + ux;
offset.p1.x = seg.p1.x - uy;
offset.p1.y = seg.p1.y + ux;
}
/**
* Add an end cap around point p1, terminating a line segment coming from p0
*/
public void addLineEndCap(Coordinate p0, Coordinate p1)
{
LineSegment seg = new LineSegment(p0, p1);
LineSegment offsetL = new LineSegment();
computeOffsetSegment(seg, Position.LEFT, distance, offsetL);
LineSegment offsetR = new LineSegment();
computeOffsetSegment(seg, Position.RIGHT, distance, offsetR);
double dx = p1.x - p0.x;
double dy = p1.y - p0.y;
double angle = Math.atan2(dy, dx);
switch (bufParams.getEndCapStyle()) {
case BufferParameters.CAP_ROUND:
// add offset seg points with a fillet between them
segList.addPt(offsetL.p1);
addFillet(p1, angle + Math.PI / 2, angle - Math.PI / 2, CGAlgorithms.CLOCKWISE, distance);
segList.addPt(offsetR.p1);
break;
case BufferParameters.CAP_FLAT:
// only offset segment points are added
segList.addPt(offsetL.p1);
segList.addPt(offsetR.p1);
break;
case BufferParameters.CAP_SQUARE:
// add a square defined by extensions of the offset segment endpoints
Coordinate squareCapSideOffset = new Coordinate();
squareCapSideOffset.x = Math.abs(distance) * Math.cos(angle);
squareCapSideOffset.y = Math.abs(distance) * Math.sin(angle);
Coordinate squareCapLOffset = new Coordinate(
offsetL.p1.x + squareCapSideOffset.x,
offsetL.p1.y + squareCapSideOffset.y);
Coordinate squareCapROffset = new Coordinate(
offsetR.p1.x + squareCapSideOffset.x,
offsetR.p1.y + squareCapSideOffset.y);
segList.addPt(squareCapLOffset);
segList.addPt(squareCapROffset);
break;
}
}
/**
* Adds a mitre join connecting the two reflex offset segments.
* The mitre will be beveled if it exceeds the mitre ratio limit.
*
* @param offset0 the first offset segment
* @param offset1 the second offset segment
* @param distance the offset distance
*/
private void addMitreJoin(Coordinate p,
LineSegment offset0,
LineSegment offset1,
double distance)
{
boolean isMitreWithinLimit = true;
Coordinate intPt = null;
/**
* This computation is unstable if the offset segments are nearly collinear.
* However, this situation should have been eliminated earlier by the check for
* whether the offset segment endpoints are almost coincident
*/
try {
intPt = HCoordinate.intersection(offset0.p0,
offset0.p1, offset1.p0, offset1.p1);
double mitreRatio = distance <= 0.0 ? 1.0
: intPt.distance(p) / Math.abs(distance);
if (mitreRatio > bufParams.getMitreLimit())
isMitreWithinLimit = false;
}
catch (NotRepresentableException ex) {
intPt = new Coordinate(0,0);
isMitreWithinLimit = false;
}
if (isMitreWithinLimit) {
segList.addPt(intPt);
}
else {
addLimitedMitreJoin(offset0, offset1, distance, bufParams.getMitreLimit());
// addBevelJoin(offset0, offset1);
}
}
/**
* Adds a limited mitre join connecting the two reflex offset segments.
* A limited mitre is a mitre which is beveled at the distance
* determined by the mitre ratio limit.
*
* @param offset0 the first offset segment
* @param offset1 the second offset segment
* @param distance the offset distance
* @param mitreLimit the mitre limit ratio
*/
private void addLimitedMitreJoin(
LineSegment offset0,
LineSegment offset1,
double distance,
double mitreLimit)
{
Coordinate basePt = seg0.p1;
double ang0 = Angle.angle(basePt, seg0.p0);
double ang1 = Angle.angle(basePt, seg1.p1);
// oriented angle between segments
double angDiff = Angle.angleBetweenOriented(seg0.p0, basePt, seg1.p1);
// half of the interior angle
double angDiffHalf = angDiff / 2;
// angle for bisector of the interior angle between the segments
double midAng = Angle.normalize(ang0 + angDiffHalf);
// rotating this by PI gives the bisector of the reflex angle
double mitreMidAng = Angle.normalize(midAng + Math.PI);
// the miterLimit determines the distance to the mitre bevel
double mitreDist = mitreLimit * distance;
// the bevel delta is the difference between the buffer distance
// and half of the length of the bevel segment
double bevelDelta = mitreDist * Math.abs(Math.sin(angDiffHalf));
double bevelHalfLen = distance - bevelDelta;
// compute the midpoint of the bevel segment
double bevelMidX = basePt.x + mitreDist * Math.cos(mitreMidAng);
double bevelMidY = basePt.y + mitreDist * Math.sin(mitreMidAng);
Coordinate bevelMidPt = new Coordinate(bevelMidX, bevelMidY);
// compute the mitre midline segment from the corner point to the bevel segment midpoint
LineSegment mitreMidLine = new LineSegment(basePt, bevelMidPt);
// finally the bevel segment endpoints are computed as offsets from
// the mitre midline
Coordinate bevelEndLeft = mitreMidLine.pointAlongOffset(1.0, bevelHalfLen);
Coordinate bevelEndRight = mitreMidLine.pointAlongOffset(1.0, -bevelHalfLen);
if (side == Position.LEFT) {
segList.addPt(bevelEndLeft);
segList.addPt(bevelEndRight);
}
else {
segList.addPt(bevelEndRight);
segList.addPt(bevelEndLeft);
}
}
/**
* Adds a bevel join connecting the two offset segments
* around a reflex corner.
*
* @param offset0 the first offset segment
* @param offset1 the second offset segment
*/
private void addBevelJoin(
LineSegment offset0,
LineSegment offset1)
{
segList.addPt(offset0.p1);
segList.addPt(offset1.p0);
}
/**
* Add points for a circular fillet around a reflex corner.
* Adds the start and end points
*
* @param p base point of curve
* @param p0 start point of fillet curve
* @param p1 endpoint of fillet curve
* @param direction the orientation of the fillet
* @param radius the radius of the fillet
*/
private void addFillet(Coordinate p, Coordinate p0, Coordinate p1, int direction, double radius)
{
double dx0 = p0.x - p.x;
double dy0 = p0.y - p.y;
double startAngle = Math.atan2(dy0, dx0);
double dx1 = p1.x - p.x;
double dy1 = p1.y - p.y;
double endAngle = Math.atan2(dy1, dx1);
if (direction == CGAlgorithms.CLOCKWISE) {
if (startAngle <= endAngle) startAngle += 2.0 * Math.PI;
}
else { // direction == COUNTERCLOCKWISE
if (startAngle >= endAngle) startAngle -= 2.0 * Math.PI;
}
segList.addPt(p0);
addFillet(p, startAngle, endAngle, direction, radius);
segList.addPt(p1);
}
/**
* Adds points for a circular fillet arc
* between two specified angles.
* The start and end point for the fillet are not added -
* the caller must add them if required.
*
* @param direction is -1 for a CW angle, 1 for a CCW angle
* @param radius the radius of the fillet
*/
private void addFillet(Coordinate p, double startAngle, double endAngle, int direction, double radius)
{
int directionFactor = direction == CGAlgorithms.CLOCKWISE ? -1 : 1;
double totalAngle = Math.abs(startAngle - endAngle);
int nSegs = (int) (totalAngle / filletAngleQuantum + 0.5);
if (nSegs < 1) return; // no segments because angle is less than increment - nothing to do!
double initAngle, currAngleInc;
// choose angle increment so that each segment has equal length
initAngle = 0.0;
currAngleInc = totalAngle / nSegs;
double currAngle = initAngle;
Coordinate pt = new Coordinate();
while (currAngle < totalAngle) {
double angle = startAngle + directionFactor * currAngle;
pt.x = p.x + radius * Math.cos(angle);
pt.y = p.y + radius * Math.sin(angle);
segList.addPt(pt);
currAngle += currAngleInc;
}
}
/**
* Creates a CW circle around a point
*/
public void createCircle(Coordinate p)
{
// add start point
Coordinate pt = new Coordinate(p.x + distance, p.y);
segList.addPt(pt);
addFillet(p, 0.0, 2.0 * Math.PI, -1, distance);
segList.closeRing();
}
/**
* Creates a CW square around a point
*/
public void createSquare(Coordinate p)
{
segList.addPt(new Coordinate(p.x + distance, p.y + distance));
segList.addPt(new Coordinate(p.x + distance, p.y - distance));
segList.addPt(new Coordinate(p.x - distance, p.y - distance));
segList.addPt(new Coordinate(p.x - distance, p.y + distance));
segList.closeRing();
}
}