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Path intersections: support DivideBy
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@tdewolff
tdewolff committed Jan 21, 2025
1 parent 45e3289 commit 095c872
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Showing 2 changed files with 69 additions and 56 deletions.
90 changes: 51 additions & 39 deletions path_intersection.go
View file
Original file line number Diff line number Diff line change
Expand Up @@ -87,7 +87,7 @@ const (
opOR
opNOT
opXOR
//opDIV
opDIV
)

func (op pathOp) String() string {
Expand All @@ -102,6 +102,8 @@ func (op pathOp) String() string {
return "NOT"
case opXOR:
return "XOR"
case opDIV:
return "DIV"
}
return fmt.Sprintf("pathOp(%d)", op)
}
Expand Down Expand Up @@ -189,14 +191,14 @@ func (ps Paths) Not(qs Paths) *Path {
// split into subpaths if possible. Note that path p is flattened unless q is already flat. Path
// q is implicitly closed. It runs in O((n + k) log n), with n the sum of the number of segments,
// and k the number of intersections.
//func (p *Path) DivideBy(q *Path) *Path {
// return bentleyOttmann(p.Split(), q.Split(), opDIV, NonZero)
//}
//
//// DivideBy is the same as Path.DivideBy, but faster if paths are already split.
//func (ps Paths) DivideBy(qs Paths) *Path {
// return bentleyOttmann(ps, qs, opDIV, NonZero)
//}
func (p *Path) DivideBy(q *Path) *Path {
return bentleyOttmann(p.Split(), q.Split(), opDIV, NonZero)
}

// DivideBy is the same as Path.DivideBy, but faster if paths are already split.
func (ps Paths) DivideBy(qs Paths) *Path {
return bentleyOttmann(ps, qs, opDIV, NonZero)
}

type SweepPoint struct {
// initial data
Expand All @@ -219,14 +221,13 @@ type SweepPoint struct {
resultWindings int // windings of the resulting polygon

// bools at the end to optimize memory layout of struct
clipping bool // is clipping path (otherwise is subject path)
open bool // path is not closed (only for subject paths)
left bool // point is left-end of segment
vertical bool // segment is vertical
increasing bool // original direction is left-right (or bottom-top)
overlapped bool // segment's overlapping was handled
inResult bool // in final result polygon
processed bool // written to final path
clipping bool // is clipping path (otherwise is subject path)
open bool // path is not closed (only for subject paths)
left bool // point is left-end of segment
vertical bool // segment is vertical
increasing bool // original direction is left-right (or bottom-top)
overlapped bool // segment's overlapping was handled
inResult uint8 // in final result polygon (1 is once, 2 is twice for opDIV)
}

func (s *SweepPoint) InterpolateY(x float64) float64 {
Expand Down Expand Up @@ -1593,7 +1594,7 @@ func (cur *SweepPoint) computeSweepFields(prev *SweepPoint, op pathOp, fillRule
cur.other.inResult = cur.inResult
}

func (s *SweepPoint) InResult(op pathOp, fillRule FillRule) bool {
func (s *SweepPoint) InResult(op pathOp, fillRule FillRule) uint8 {
lowerWindings, lowerOtherWindings := s.windings, s.otherWindings
upperWindings, upperOtherWindings := s.windings+s.selfWindings, s.otherWindings+s.otherSelfWindings
if s.clipping {
Expand All @@ -1604,13 +1605,18 @@ func (s *SweepPoint) InResult(op pathOp, fillRule FillRule) bool {
if s.open {
// handle open paths on the subject
switch op {
case opSettle, opOR:
return true
case opSettle, opOR, opDIV:
return 1
case opAND:
return fillRule.Fills(lowerOtherWindings) || fillRule.Fills(upperOtherWindings)
if fillRule.Fills(lowerOtherWindings) || fillRule.Fills(upperOtherWindings) {
return 1
}
case opNOT, opXOR:
return !fillRule.Fills(lowerOtherWindings) || !fillRule.Fills(upperOtherWindings)
if !fillRule.Fills(lowerOtherWindings) || !fillRule.Fills(upperOtherWindings) {
return 1
}
}
return 0
}

// lower/upper windings refers to subject path, otherWindings to clipping path
Expand All @@ -1631,14 +1637,22 @@ func (s *SweepPoint) InResult(op pathOp, fillRule FillRule) bool {
case opXOR:
belowFills = fillRule.Fills(lowerWindings) != fillRule.Fills(lowerOtherWindings)
aboveFills = fillRule.Fills(upperWindings) != fillRule.Fills(upperOtherWindings)
//case opDIV:
// belowFills = fillRule.Fills(lowerWindings)
// aboveFills = fillRule.Fills(upperWindings)
// return belowFills|| aboveFills
case opDIV:
belowFills = fillRule.Fills(lowerWindings)
aboveFills = fillRule.Fills(upperWindings)
if belowFills && aboveFills {
return 2
} else if belowFills || aboveFills {
return 1
}
return 0
}

// only keep edge if there is a change in filling between both sides
return belowFills != aboveFills
if belowFills != aboveFills {
return 1
}
return 0
}

func (s *SweepPoint) mergeOverlapping(op pathOp, fillRule FillRule) {
Expand Down Expand Up @@ -1668,7 +1682,7 @@ func (s *SweepPoint) mergeOverlapping(op pathOp, fillRule FillRule) {
s.otherSelfWindings += prev.selfWindings
}
prev.windings, prev.selfWindings, prev.otherWindings, prev.otherSelfWindings = 0, 0, 0, 0
prev.inResult, prev.other.inResult = false, false
prev.inResult, prev.other.inResult = 0, 0
prev.overlapped = true
}
if prev == s.prev {
Expand Down Expand Up @@ -2170,19 +2184,15 @@ func bentleyOttmann(ps, qs Paths, op pathOp, fillRule FillRule) *Path {
var Ropen *Path
for _, square := range squares {
for _, cur := range square.Events {
if !cur.inResult || cur.processed {
if cur.inResult == 0 {
continue
}

BuildPath:
windings := 0
prev := cur.prev
for prev != nil {
if prev.inResult {
windings = prev.resultWindings
break
}
prev = prev.prev
if op != opDIV && prev != nil {
windings = prev.resultWindings
}

first := cur
Expand Down Expand Up @@ -2215,7 +2225,7 @@ func bentleyOttmann(ps, qs Paths, op pathOp, fillRule FillRule) *Path {
}
if i == i0 {
break
} else if nodes[i].inResult && !nodes[i].processed && nodes[i].open == first.open {
} else if 0 < nodes[i].inResult && nodes[i].open == first.open {
next = nodes[i]
break
}
Expand All @@ -2242,9 +2252,11 @@ func bentleyOttmann(ps, qs Paths, op pathOp, fillRule FillRule) *Path {
cur.resultWindings++
}
cur.other.resultWindings = cur.resultWindings
cur.processed, cur.other.processed = true, true
cur.other.inResult--
cur.inResult--
}
first.processed, first.other.processed = true, true
first.other.inResult--
first.inResult--

if first.open {
if Ropen != nil {
Expand All @@ -2254,7 +2266,7 @@ func bentleyOttmann(ps, qs Paths, op pathOp, fillRule FillRule) *Path {
Ropen = nil
} else {
for _, cur2 := range square.Events {
if cur2.inResult && !cur2.processed && cur2.open {
if 0 < cur2.inResult && cur2.open {
cur = cur2
Ropen = &Path{d: make([]float64, len(R.d)-indexR-4)}
copy(Ropen.d, R.d[indexR+4:])
Expand Down
35 changes: 18 additions & 17 deletions path_intersection_test.go
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1816,20 +1816,21 @@ func TestPathNot(t *testing.T) {
}
}

//func TestPathDivideBy(t *testing.T) {
// var tts = []struct {
// p, q string
// r string
// }{
// {"L10 0L5 10z", "M0 5L10 5L5 15z", "L10 0L7.5 5L2.5 5zM2.5 5L7.5 5L5 10z"},
// {"L2 0L2 2L0 2zM4 0L6 0L6 2L4 2z", "M1 1L5 1L5 3L1 3z", "M0 0L2 0L2 1L1 1L1 2L0 2zM1 1L2 1L2 2L1 2zM4 0L6 0L6 2L5 2L5 1L4 1zM4 1L5 1L5 2L4 2z"},
// {"L2 0L2 2L0 2zM4 0L6 0L6 2L4 2z", "M1 1L1 3L5 3L5 1z", "M0 0L2 0L2 1L1 1L1 2L0 2zM1 1L2 1L2 2L1 2zM4 0L6 0L6 2L5 2L5 1L4 1zM4 1L5 1L5 2L4 2z"},
// }
// for _, tt := range tts {
// t.Run(fmt.Sprint(tt.p, "x", tt.q), func(t *testing.T) {
// p := MustParseSVGPath(tt.p)
// q := MustParseSVGPath(tt.q)
// test.T(t, p.DivideBy(q), MustParseSVGPath(tt.r))
// })
// }
//}
func TestPathDivideBy(t *testing.T) {
var tts = []struct {
p, q string
r string
}{
{"L10 0L5 10z", "M0 5L10 5L5 15z", "L10 0L7.5 5L2.5 5zM2.5 5L7.5 5L5 10z"},
{"L2 0L2 2L0 2zM4 0L6 0L6 2L4 2z", "M1 1L5 1L5 3L1 3z", "M0 0L2 0L2 1L1 1L1 2L0 2zM1 1L2 1L2 2L1 2zM4 0L6 0L6 2L5 2L5 1L4 1zM4 1L5 1L5 2L4 2z"},
{"L2 0L2 2L0 2zM4 0L6 0L6 2L4 2z", "M1 1L1 3L5 3L5 1z", "M0 0L2 0L2 1L1 1L1 2L0 2zM1 1L2 1L2 2L1 2zM4 0L6 0L6 2L5 2L5 1L4 1zM4 1L5 1L5 2L4 2z"},
}
for _, tt := range tts {
t.Run(fmt.Sprint(tt.p, "x", tt.q), func(t *testing.T) {
p := MustParseSVGPath(tt.p)
q := MustParseSVGPath(tt.q)
r := p.DivideBy(q)
test.T(t, r, MustParseSVGPath(tt.r))
})
}
}

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