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segment.go
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segment.go
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package slice
import (
"fmt"
"math"
"sigint.ca/slice/vector"
)
var errNoIntersections = fmt.Errorf("no intersections")
var errOutOfBounds = fmt.Errorf("line out of bounds")
// Segments can represent both perimeter and infill lines
type Segment struct {
From, To Vertex2 // ordered so that gcode movements are from "from" to "to"
Normal vector.V2 // points to the inside of the solid
line *line // hold on to the slope and y-intercept of the line once calculated
}
func (s *Segment) String() string {
return fmt.Sprintf("%v-%v", s.From, s.To)
}
func (s *Segment) Length() float64 {
dx := s.To.X - s.From.Y
dy := s.To.Y - s.From.Y
return math.Sqrt(dx*dx + dy*dy)
}
func (s *Segment) getLine() *line {
if s.line != nil {
return s.line
}
div := s.To.X - s.From.X
var slope float64
if div == 0 {
slope = math.Inf(+1)
s.line = &line{m: slope, b: s.To.X}
} else {
slope = (s.To.Y - s.From.Y) / div
s.line = &line{m: slope, b: s.From.Y - slope*s.From.X}
}
return s.line
}
func (s *Segment) ShiftBy(v vector.V2) *Segment {
s.From = Vertex2(vector.V2(s.From).Add(v))
s.To = Vertex2(vector.V2(s.To).Add(v))
s.line = nil
return s
}
func (s *Segment) intersect(ss *Segment) (Vertex2, bool) {
if s.From.touches(ss.From) ||
s.From.touches(ss.To) ||
s.To.touches(ss.From) ||
s.To.touches(ss.To) {
return Vertex2{}, false
}
// eliminate cases where the Segments do not have overlapping X coordinates
if math.Max(s.From.X, s.To.X) < math.Min(ss.From.X, ss.To.X) {
return Vertex2{}, false
}
if math.Min(s.From.X, s.To.X) > math.Max(ss.From.X, ss.To.X) {
return Vertex2{}, false
}
l1, l2 := s.getLine(), ss.getLine()
if approxEquals(l1.m, l2.m, 0.000001) {
// l1 and l2 are parallel
return Vertex2{}, false
}
// calculate point of intersection
// TODO: duplicate of line.intersect?
var v Vertex2
if math.IsInf(l1.m, 0) {
// ray is vertical
v.X = s.From.X
v.Y = l2.m*v.X + l2.b
if !inRange(v.Y, ss.From.Y, ss.To.Y) {
return Vertex2{}, false
}
} else if math.IsInf(l2.m, 0) {
// s is vertical
v.X = ss.From.X
v.Y = l1.m*v.X + l1.b
if !inRange(v.Y, ss.From.Y, ss.To.Y) {
return Vertex2{}, false
}
} else {
v.X = (l2.b - l1.b) / (l1.m - l2.m)
v.Y = l1.m*v.X + l1.b // doesn't matter which line we use in this case
if !inRange(v.X, ss.From.X, ss.To.X) {
return Vertex2{}, false
}
}
return v, true
}
// getIntersections returns a list of Segments in target that intersect with ray, as well
// as a list of the corresponding intersection points.
func (ray *Segment) getIntersections(target []*Segment) ([]*Segment, []Vertex2) {
intersecting := make([]*Segment, 0)
points := make([]Vertex2, 0)
for _, s := range target {
v, ok := ray.intersect(s)
if !ok {
continue
}
intersecting = append(intersecting, s)
points = append(points, v)
}
return intersecting, points
}
// checkDomain returns true if v is within the domain x1..x2, or false otherwise
func inRange(test, v1, v2 float64) bool {
return test >= math.Min(v1, v2)-0.000001 && test <= math.Max(v1, v2)+0.000001
}
type line struct {
m float64 // slope of line (calculated)
b float64 // y intercept (calculated) (or x value if m is infinite)
}
func (l *line) String() string {
if math.IsInf(l.m, 0) {
return fmt.Sprintf("vertical line at x=%v", l.b)
}
return fmt.Sprintf("(y=%.1fx+%.1f", l.m, l.b)
}
func lineFromAngle(origin Vertex2, angle float64) *line {
slope := math.Tan(angle)
return &line{m: slope, b: origin.Y - slope*origin.X}
}
func (l1 *line) intersect(l2 *line) (Vertex2, error) {
if *l1 == *l2 {
return Vertex2{}, errNoIntersections
}
var x, y float64
if math.IsInf(l1.m, 0) && math.IsInf(l2.m, 0) {
return Vertex2{}, errNoIntersections
}
if math.IsInf(l1.m, 0) {
x = l1.b
y = l2.m*x + l2.b // l2 is not vertical
} else if math.IsInf(l2.m, 0) {
x = l2.b
y = l1.m*x + l1.b // l1 is not vertical
} else {
div := l1.m - l2.m
if div == 0 {
return Vertex2{}, errNoIntersections
}
x = (l2.b - l1.b) / div
y = l1.m*x + l1.b // doesn't matter which line is used here
}
return Vertex2{X: x, Y: y}, nil
}
// bound returns a Segment representing the line bounded by the rectangle (min-max)
func (l *line) bound(min, max Vertex2) (*Segment, error) {
left := &Segment{From: min, To: Vertex2{X: min.X, Y: max.Y}}
right := &Segment{From: Vertex2{X: max.X, Y: min.Y}, To: max}
top := &Segment{From: min, To: Vertex2{X: max.X, Y: min.Y}}
bottom := &Segment{From: Vertex2{X: min.X, Y: max.Y}, To: max}
ends := make([]Vertex2, 0, 2)
v1, err := left.getLine().intersect(l)
if err == nil && inRange(v1.Y, left.From.Y, left.To.Y) {
ends = append(ends, v1)
}
v2, err := right.getLine().intersect(l)
if err == nil && inRange(v2.Y, right.From.Y, right.To.Y) {
ends = append(ends, v2)
}
v3, err := top.getLine().intersect(l)
if err == nil && inRange(v3.X, top.From.X, top.To.X) && !v3.touches(v1) && !v3.touches(v2) {
ends = append(ends, v3)
}
v4, err := bottom.getLine().intersect(l)
if err == nil && inRange(v4.X, bottom.From.X, bottom.To.X) && !v4.touches(v1) && !v4.touches(v2) {
ends = append(ends, v4)
}
if len(ends) != 2 {
return nil, errOutOfBounds
}
return &Segment{
From: ends[0],
To: ends[1],
line: l,
}, nil
}