// Copyright 2018 Joshua J Baker. All rights reserved. // Use of this source code is governed by an MIT-style // license that can be found in the LICENSE file. package geometry import ( "math" ) const complexRingMinPoints = 16 // Ring ... type Ring = Series func newRing(points []Point, index int) Ring { series := makeSeries(points, true, true, index) return &series } type ringResult struct { hit bool // contains/intersects idx int // edge index } func ringContainsPoint(ring Ring, point Point, allowOnEdge bool) ringResult { // println("A") var idx = -1 // find all intersecting segments on the y-axis var in bool ring.Search( Rect{Point{math.Inf(-1), point.Y}, Point{math.Inf(+1), point.Y}}, func(seg Segment, index int) bool { // fmt.Printf("%v %v\n", point, seg) // perform a raycast operation on the segments res := seg.Raycast(point) if res.On { // println(1) in = allowOnEdge idx = index return false } if res.In { // println(2) in = !in } return true }, ) return ringResult{hit: in, idx: idx} } func ringIntersectsPoint(ring Ring, point Point, allowOnEdge bool) ringResult { return ringContainsPoint(ring, point, allowOnEdge) } // func segmentsIntersects(seg, other Segment, allowOnEdge bool) bool { // if seg.IntersectsSegment(other) { // } // return false // } func ringContainsSegment(ring Ring, seg Segment, allowOnEdge bool) bool { // fmt.Printf("%v %v\n", seg.A, seg.B) // Test that segment points are contained in the ring. resA := ringContainsPoint(ring, seg.A, allowOnEdge) if !resA.hit { // seg A is not inside ring return false } if seg.B == seg.A { return true } resB := ringContainsPoint(ring, seg.B, allowOnEdge) if !resB.hit { // seg B is not inside ring return false } if ring.Convex() { // ring is convex so the segment must be contained return true } // The ring is concave so it's possible that the segment crosses over the // edge of the ring. if allowOnEdge { // do some logic around seg points that are on the edge of the ring. if resA.idx != -1 { // seg A is on a ring segment if resB.idx != -1 { // seg B is on a ring segment if resB.idx == resA.idx { // case (3) // seg A and B share the same ring segment, so it must be // on the inside. return true } // case (1) // seg A and seg B are on different segments. // determine if the space that the seg passes over is inside or // outside of the ring. To do so we create a ring from the two // ring segments and check if that ring winding order matches // the winding order of the ring. // -- create a ring rSegA := ring.SegmentAt(resA.idx) rSegB := ring.SegmentAt(resB.idx) if rSegA.A == seg.A || rSegA.B == seg.A || rSegB.A == seg.A || rSegB.B == seg.A || rSegA.A == seg.B || rSegA.B == seg.B || rSegB.A == seg.B || rSegB.B == seg.B { return true } // fix the order of the if resB.idx < resA.idx { rSegA, rSegB = rSegB, rSegA } pts := [5]Point{rSegA.A, rSegA.B, rSegB.A, rSegB.B, rSegA.A} // -- calc winding order var cwc float64 for i := 0; i < len(pts)-1; i++ { a, b := pts[i], pts[i+1] cwc += (b.X - a.X) * (b.Y + a.Y) } clockwise := cwc > 0 if clockwise != ring.Clockwise() { // -- on the outside return false } // the passover space is on the inside of the ring. // check if seg intersects any ring segments where A and B are // not on. var intersects bool ring.Search(seg.Rect(), func(seg2 Segment, index int) bool { if seg.IntersectsSegment(seg2) { if !seg2.Raycast(seg.A).On && !seg2.Raycast(seg.B).On { intersects = true return false } } return true }) return !intersects } // case (4) // seg A is on a ring segment, but seg B is not. // check if seg intersects any ring segments where A is not on. var intersects bool ring.Search(seg.Rect(), func(seg2 Segment, index int) bool { if seg.IntersectsSegment(seg2) { if !seg2.Raycast(seg.A).On { intersects = true return false } } return true }) return !intersects } else if resB.idx != -1 { // case (2) // seg B is on a ring segment, but seg A is not. // check if seg intersects any ring segments where B is not on. var intersects bool ring.Search(seg.Rect(), func(seg2 Segment, index int) bool { if seg.IntersectsSegment(seg2) { if !seg2.Raycast(seg.B).On { intersects = true return false } } return true }) return !intersects } // case (5) (15) var intersects bool ring.Search(seg.Rect(), func(seg2 Segment, index int) bool { if seg.IntersectsSegment(seg2) { if !seg.Raycast(seg2.A).On && !seg.Raycast(seg2.B).On { intersects = true return false } } return true }) return !intersects } // allowOnEdge is false. (not allow on edge) var intersects bool ring.Search(seg.Rect(), func(seg2 Segment, index int) bool { if seg.IntersectsSegment(seg2) { // if seg.Raycast(seg2.A).On || seg.Raycast(seg2.B).On { intersects = true // return false // } return false } return true }) return !intersects } // ringIntersectsSegment detect if the segment intersects the ring func ringIntersectsSegment(ring Ring, seg Segment, allowOnEdge bool) bool { // Quick check that either point is inside of the ring if ringContainsPoint(ring, seg.A, allowOnEdge).hit { return true } if ringContainsPoint(ring, seg.B, allowOnEdge).hit { return true } // Neither point A or B is inside the the ring. It's possible that both // are on the outside and are passing over segments. If the segment passes // over at least two ring segments then it's intersecting. var count int var segAOn bool var segBOn bool ring.Search(seg.Rect(), func(seg2 Segment, index int) bool { if seg.IntersectsSegment(seg2) { if !allowOnEdge { // for segments that are not allowed on the edge, extra care // must be taken. if !(seg.CollinearPoint(seg2.A) && seg.CollinearPoint(seg2.B)) { if !segAOn { if seg.A == seg2.A || seg.A == seg2.B { segAOn = true return true } } if !segBOn { if seg.B == seg2.A || seg.B == seg2.B { segBOn = true return true } } count++ } } else { count++ } } return count < 2 }) return count >= 2 } func ringContainsRing(ring, other Ring, allowOnEdge bool) bool { if ring.Empty() || other.Empty() { return false } if other.NumPoints() >= complexRingMinPoints { // inner ring has a lot of points, and is convex, so let just check if // the rect ring is fully contained before we do the complicated stuff. if ringContainsRing(ring, other.Rect(), allowOnEdge) { return true } } // test if the inner rect does not contain the outer rect if !ring.Rect().ContainsRect(other.Rect()) { // not contained so it's not possible for the outer ring to contain // the inner ring return false } if ring.Convex() { // outer ring is convex so test that all inner points are inside of // the outer ring otherNumPoints := other.NumPoints() for i := 0; i < otherNumPoints; i++ { if !ringContainsPoint(ring, other.PointAt(i), allowOnEdge).hit { // point is on the outside the outer ring return false } } } else { // outer ring is concave so let's make sure that all inner segments are // fully contained inside of the outer ring. otherNumSegments := other.NumSegments() for i := 0; i < otherNumSegments; i++ { if !ringContainsSegment(ring, other.SegmentAt(i), allowOnEdge) { // fmt.Printf("%v %v\n", ring, other.SegmentAt(i)) return false } } } return true } func ringIntersectsRing(ring, other Ring, allowOnEdge bool) bool { if ring.Empty() || other.Empty() { return false } // check outer and innter rects intersection first if !ring.Rect().IntersectsRect(other.Rect()) { return false } if other.Rect().Area() > ring.Rect().Area() { // swap the rings so that the inner ring is smaller than the outer ring ring, other = other, ring } if ring.Convex() && allowOnEdge { // outer ring is convex so test that any inner points are inside of // the outer ring otherNumPoints := other.NumPoints() for i := 0; i < otherNumPoints; i++ { if ringContainsPoint(ring, other.PointAt(i), allowOnEdge).hit { return true } } } else { // outer ring is concave so let's make sure that all inner segments are // fully contained inside of the outer ring. otherNumSegments := other.NumSegments() for i := 0; i < otherNumSegments; i++ { if ringIntersectsSegment(ring, other.SegmentAt(i), allowOnEdge) { return true } } } return false } func ringContainsLine(ring Ring, line *Line, allowOnEdge bool) bool { // shares the same logic return ringContainsRing(ring, Ring(&line.baseSeries), allowOnEdge) } func ringIntersectsLine(ring Ring, line *Line, allowOnEdge bool) bool { if ring.Empty() || line.Empty() { return false } // check outer and innter rects intersection first if !ring.Rect().IntersectsRect(line.Rect()) { return false } // check if any points are inside ring lineNumPoints := line.NumPoints() for i := 0; i < lineNumPoints; i++ { if ringContainsPoint(ring, line.PointAt(i), allowOnEdge).hit { return true } } lineNumSegments := line.NumSegments() for i := 0; i < lineNumSegments; i++ { if ringIntersectsSegment(ring, line.SegmentAt(i), allowOnEdge) { return true } } return false }