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Copy pathrect.go
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708 lines (633 loc) · 16.7 KB
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// SPDX-FileCopyrightText: 2018 Raph Levien
// SPDX-FileCopyrightText: 2024 Dominik Honnef and contributors
//
// SPDX-License-Identifier: MIT
// SPDX-FileAttributionText: https://github.com/linebender/kurbo
package curve
import (
"math"
)
// Rect describes a rectangle defined by its minimum and maximum coordinates.
//
// It is possible to construct rectangles with negative width or height. Many
// functions will treat rectangles that have at least one negative dimension as
// non-existent. Such rectangles cannot overlap, intersect, or union with other
// rectangles, among other things.
//
// [Rect.Area] does return meaningful values for rectangles with negative
// dimensions, since it is defined as width × height. If exactly one of the
// dimensions is negative, the area will be, too.
type Rect struct {
X0, Y0 float64
X1, Y1 float64
}
var _ ClosedShape = Rect{}
// NewRectFromPoints returns a rectangle with the extents of p0 and p1, ensuring that
// width and height are non-negative.
func NewRectFromPoints(p0, p1 Point) Rect {
return Rect{p0.X, p0.Y, p1.X, p1.Y}.Abs()
}
// NewRectFromOrigin returns a rectangle with the given size, extending to the right and
// down (for positive sizes) from the origin. Width and height are ensured to be
// non-negative.
func NewRectFromOrigin(origin Point, size Size) Rect {
return NewRectFromPoints(origin, origin.Translate(Vec2(size.AsVec2())))
}
// NewRectFromCenter returns a rectangle with the given size, centered around the center
// point.
func NewRectFromCenter(center Point, size Size) Rect {
return Rect{
X0: center.X - size.Width/2,
Y0: center.Y - size.Height/2,
X1: center.X + size.Width/2,
Y1: center.Y + size.Height/2,
}
}
// WithOrigin returns a new rectangle with the same size as r and a new origin.
func (r Rect) WithOrigin(origin Point) Rect {
return NewRectFromOrigin(origin, r.Size())
}
// WithSize returns a new rectangle with the same origin as r and a new size.
func (r Rect) WithSize(size Size) Rect {
return NewRectFromOrigin(r.Origin(), size)
}
// Inset applies insets to r.
//
// The operation is performed on r.Abs(), so it does not preserve negative width
// or height in the input rectangle.
func (r Rect) Inset(insets Insets) Rect {
return insets.Apply(r)
}
// Sub computes the insets that transform o into r.
func (r Rect) Sub(o Rect) Insets {
return Insets{
X0: o.X0 - r.X0,
Y0: o.Y0 - r.Y0,
X1: r.X1 - o.X1,
Y1: r.Y1 - o.Y1,
}
}
// Abs returns a new rectangle with the same extents as r, but ensuring that width and
// height are non-negative.
func (r Rect) Abs() Rect {
return Rect{
X0: min(r.X0, r.X1),
Y0: min(r.Y0, r.Y1),
X1: max(r.X0, r.X1),
Y1: max(r.Y0, r.Y1),
}
}
func (r Rect) MinX() float64 { return min(r.X0, r.X1) }
func (r Rect) MaxX() float64 { return max(r.X0, r.X1) }
func (r Rect) MinY() float64 { return min(r.Y0, r.Y1) }
func (r Rect) MaxY() float64 { return max(r.Y0, r.Y1) }
// Origin returns the origin of the rectangle.
//
// This is the top left corner in a y-down space and with
// non-negative width and height.
func (r Rect) Origin() Point {
return Point{
X: r.X0,
Y: r.Y0,
}
}
// Width returns the rectangle's width, defined as X1 − X0. It may be negative.
func (r Rect) Width() float64 {
return r.X1 - r.X0
}
// Height returns the rectangle's heigth, defined as Y1 − Y0. It may be negative.
func (r Rect) Height() float64 {
return r.Y1 - r.Y0
}
func (r Rect) Size() Size {
return Size{
Width: r.Width(),
Height: r.Height(),
}
}
func (r Rect) Center() Point {
return Point{
X: 0.5 * (r.X0 + r.X1),
Y: 0.5 * (r.Y0 + r.Y1),
}
}
// Contains reports whether r contains the point pt.
//
// Non-existent rectangles do not contain any points.
func (r Rect) Contains(pt Point) bool {
return pt.X >= r.X0 &&
pt.X < r.X1 &&
pt.Y >= r.Y0 &&
pt.Y < r.Y1
}
// ContainsRect reports whether r contains the rectangle o.
//
// Two identical rectangles contain each other.
//
// Non-existent rectangles can neither contain nor be contained by other
// rectangles.
func (r Rect) ContainsRect(o Rect) bool {
if !r.Exists() || !o.Exists() {
return false
}
return r.X0 <= o.X0 && r.Y0 <= o.Y0 &&
r.X1 >= o.X1 && r.Y1 >= o.Y1
}
// Overlaps reports whether r and o overlap. Two rectangles overlap if their
// intersection is non-empty.
func (r Rect) Overlaps(o Rect) bool {
return min(r.X1, o.X1) > max(r.X0, o.X0) &&
min(r.Y1, o.Y1) > max(r.Y0, o.Y0)
}
// Union returns the smallest rectangle enclosing r and o.
//
// If one of r or o is non-existent, the other will be returned. If both are
// non-existent, the result will be some not further defined non-existent
// rectangle.
func (r Rect) Union(o Rect) Rect {
if !r.Exists() {
return o
}
if !o.Exists() {
return r
}
return Rect{
X0: min(r.X0, o.X0),
Y0: min(r.Y0, o.Y0),
X1: max(r.X1, o.X1),
Y1: max(r.Y1, o.Y1),
}
}
// UnionPoint computes the union with one point.
//
// Rectangles with no area still contribute to the result. For example:
//
// r := Rect{0, 0, 0, 0}
// pt := Point{2, 2}
// r2 := r.UnionPoint(pt)
// // r2 == Rect{0, 0, 2, 2}
//
// Non-existant rectangles, on the other hand, do not contribute to the result.
// For example:
//
// r := Rect{1, 1, 0, 0}
// pt := Point{2, 2}
// r2 := r.UnionPoint(pt)
// // r2 == Rect{2, 2, 2, 2}
func (r Rect) UnionPoint(pt Point) Rect {
if !r.Exists() {
return NewRectFromPoints(pt, pt)
}
return Rect{
X0: min(r.X0, pt.X),
Y0: min(r.Y0, pt.Y),
X1: max(r.X1, pt.X),
Y1: max(r.Y1, pt.Y),
}
}
// Intersect returns the intersection of two rectangles.
//
// The result is zero-area if either input has negative width or
// height. The result always has non-negative width and height.
func (r Rect) Intersect(o Rect) Rect {
if !r.Exists() || !o.Exists() {
return Rect{1, 1, 0, 0}
}
x0 := max(r.X0, o.X0)
y0 := max(r.Y0, o.Y0)
x1 := min(r.X1, o.X1)
y1 := min(r.Y1, o.Y1)
return Rect{
X0: x0,
Y0: y0,
X1: max(x0, x1),
Y1: max(y0, y1),
}
}
// Inflate expands a rectangle by a constant amount in both directions.
//
// The logic simply applies the amount in each direction. If rectangle
// area or added dimensions are negative, this could give odd results.
func (r Rect) Inflate(width, height float64) Rect {
return Rect{
X0: r.X0 - width,
Y0: r.Y0 - height,
X1: r.X1 + width,
Y1: r.Y1 + height,
}
}
// Round returns a new rectangle with each coordinate value rounded to the nearest
// integer.
func (r Rect) Round() Rect {
return Rect{
X0: math.Round(r.X0),
Y0: math.Round(r.Y0),
X1: math.Round(r.X1),
Y1: math.Round(r.Y1),
}
}
// Ceil returns a new rectangle with each coordinate value rounded to the least integer
// value greater than or equal to it.
func (r Rect) Ceil() Rect {
return Rect{
X0: math.Ceil(r.X0),
Y0: math.Ceil(r.Y0),
X1: math.Ceil(r.X1),
Y1: math.Ceil(r.Y1),
}
}
// Floor returns a new rectangle, with each coordinate value rounded down to the
// nearest integer.
func (r Rect) Floor() Rect {
return Rect{
X0: math.Floor(r.X0),
Y0: math.Floor(r.Y0),
X1: math.Floor(r.X1),
Y1: math.Floor(r.Y1),
}
}
// Expand returns a new rectangle, with each coordinate value rounded away from
// the center of the rectangle to the nearest integer, unless they are already
// an integer. That is to say this function will return the smallest possible
// rectangle with integer coordinates that is a superset of the input
// rectangle.
func (r Rect) Expand() Rect {
var x0, y0, x1, y1 float64
if r.X0 < r.X1 {
x0 = math.Floor(r.X0)
x1 = math.Ceil(r.X1)
} else {
x0 = math.Ceil(r.X0)
x1 = math.Floor(r.X1)
}
if r.Y0 < r.Y1 {
y0 = math.Floor(r.Y0)
y1 = math.Ceil(r.Y1)
} else {
y0 = math.Ceil(r.Y0)
y1 = math.Floor(r.Y1)
}
return Rect{
X0: x0,
Y0: y0,
X1: x1,
Y1: y1,
}
}
// Trunc returns a new rectangle, with each coordinate value rounded towards the
// center of the rectangle to the nearest integer, unless they are already an
// integer. That is to say this function will return the biggest possible
// rectangle with integer coordinates that is a subset of the input rectangle.
func (r Rect) Trunc() Rect {
var x0, y0, x1, y1 float64
if r.X0 < r.X1 {
x0 = math.Ceil(r.X0)
x1 = math.Floor(r.X1)
} else {
x0 = math.Floor(r.X0)
x1 = math.Ceil(r.X1)
}
if r.Y0 < r.Y1 {
y0 = math.Ceil(r.Y0)
y1 = math.Floor(r.Y1)
} else {
y0 = math.Floor(r.Y0)
y1 = math.Ceil(r.Y1)
}
return Rect{
X0: x0,
Y0: y0,
X1: x1,
Y1: y1,
}
}
// ScaleFromOrigin scales the rectangle by the factor f with respect to the
// origin (the point (0, 0)).
func (r Rect) ScaleFromOrigin(f float64) Rect {
return Rect{
X0: r.X0 * f,
Y0: r.Y0 * f,
X1: r.X1 * f,
Y1: r.Y1 * f,
}
}
// AspectRatio returns the aspect ratio of the rectangle.
//
// This is defined as the width divided by the height. It measures the
// "squareness" of the rectangle (a value of 1 is square).
//
// If the height is 0 the output will be "sign(x1 - x0) * infinity".
//
// If the width and height are 0, the result will be NaN.
func (r Rect) AspectRatio() float64 {
return r.Size().AspectRatio()
}
func (r Rect) IsInf() bool {
return math.IsInf(r.X0, 0) ||
math.IsInf(r.X1, 0) ||
math.IsInf(r.Y0, 0) ||
math.IsInf(r.Y1, 0)
}
func (r Rect) IsNaN() bool {
return math.IsNaN(r.X0) ||
math.IsNaN(r.X1) ||
math.IsNaN(r.Y0) ||
math.IsNaN(r.Y1)
}
// Exists returns true if the rectangle doesn't have any negative dimensions.
func (r Rect) Exists() bool {
return r.Width() >= 0 && r.Height() >= 0
}
func (r Rect) Translate(v Vec2) Rect {
return Rect{
X0: r.X0 + v.X,
Y0: r.Y0 + v.Y,
X1: r.X1 + v.X,
Y1: r.Y1 + v.Y,
}
}
func (r Rect) Area() float64 {
return r.Width() * r.Height()
}
func (r Rect) BoundingBox() Rect {
return r.Abs()
}
func (r Rect) PathLength(accuracy float64) float64 {
return 2 * (math.Abs(r.Width()) + math.Abs(r.Height()))
}
func (r Rect) Winding(pt Point) int {
// Note: this function is carefully designed so that if the plane is
// tiled with rectangles, the winding number will be nonzero for exactly
// one of them.
xmin := min(r.X0, r.X1)
xmax := max(r.X0, r.X1)
ymin := min(r.Y0, r.Y1)
ymax := max(r.Y0, r.Y1)
if pt.X >= xmin && pt.X < xmax && pt.Y >= ymin && pt.Y < ymax {
if r.X1 > r.X0 != (r.Y1 > r.Y0) {
return -1
} else {
return 1
}
} else {
return 0
}
}
func (r Rect) Path(tolerance float64, out BezPath) BezPath {
out.MoveTo(Pt(r.X0, r.Y0))
out.LineTo(Pt(r.X1, r.Y0))
out.LineTo(Pt(r.X1, r.Y1))
out.LineTo(Pt(r.X0, r.Y1))
out.ClosePath()
return out
}
// RoundedRect creates a new [RoundedRect] from this rectangle and the provided
// corner radii.
func (r Rect) RoundedRect(radii RoundedRectRadii) RoundedRect {
r = r.Abs()
shortestSide := min(r.Width(), r.Height())
radii = radii.Abs().Clamp(shortestSide / 2)
return RoundedRect{
Rect: r,
Radii: radii,
}
}
// ContainedRectWithAspectRatio returns the largest possible rectangle that is
// fully contained in this rectangle, with the given aspect ratio.
//
// The aspect ratio is specified fractionally, as width / height.
//
// The resulting rectangle will be centered if it is smaller than the input
// rectangle.
func (r Rect) ContainedRectWithAspectRatio(aspectRatio float64) Rect {
width, height := r.Width(), r.Height()
rAspect := width / height
// TODO the parameter 1e-9 was chosen quickly and may not be optimal.
if math.Abs(rAspect-aspectRatio) < 1e-9 {
return r
} else if math.Abs(rAspect) < math.Abs(aspectRatio) {
// shrink y to fit
newHeight := width / aspectRatio
gap := (height - newHeight) * 0.5
y0 := r.Y0 + gap
y1 := r.Y1 - gap
return Rect{r.X0, y0, r.X1, y1}
} else {
// shrink x to fit
newWidth := height * aspectRatio
gap := (width - newWidth) * 0.5
x0 := r.X0 + gap
x1 := r.X1 - gap
return Rect{x0, r.Y0, x1, r.Y1}
}
}
type RoundedRect struct {
Rect
Radii RoundedRectRadii
}
var _ ClosedShape = RoundedRect{}
func NewRoundedRect(x0, y0, x1, y1, radius float64) RoundedRect {
return RoundedRect{
Rect{x0, y0, x1, y1},
RoundedRectRadii{radius, radius, radius, radius},
}
}
func (r RoundedRect) Area() float64 {
// A corner is a quarter-circle, i.e.
// .............#
// . ######
// . #########
// . ###########
// . ############
// .#############
// ##############
// |-----r------|
// For each corner, we need to subtract the square that bounds this
// quarter-circle, and add back in the area of quarter circle.
corner := func(radius float64) float64 {
return (math.Pi/4 - 1) * radius * radius
}
// Start with the area of the bounding rectangle. For each corner,
// subtract the area of the corner under the quarter-circle, and add
// back the area of the quarter-circle.
return r.Rect.Area() +
corner(r.Radii[0]) +
corner(r.Radii[1]) +
corner(r.Radii[2]) +
corner(r.Radii[3])
}
func dropFirst[S ~[]E, E any](s S) S {
if len(s) == 0 {
return s
}
return s[1:]
}
func (r RoundedRect) Path(tolerance float64, out BezPath) BezPath {
buildArc := func(i int, center Point, ellipseRadii Vec2) {
a := Arc{
Center: center,
Radii: ellipseRadii,
StartAngle: math.Pi / 2 * float64(i),
SweepAngle: math.Pi / 2,
XRotation: 0.0,
}
out = appendPathDropMoveTo(out, tolerance, a)
}
out.MoveTo(Pt(
r.Rect.X0,
r.Rect.Y0+r.Radii[0],
))
buildArc(
2,
Point{
X: r.Rect.X0 + r.Radii[0],
Y: r.Rect.Y0 + r.Radii[0],
},
Vec2{
X: r.Radii[0],
Y: r.Radii[0],
},
)
out.LineTo(Pt(
r.Rect.X1-r.Radii[1],
r.Rect.Y0,
))
buildArc(
3,
Point{
X: r.Rect.X1 - r.Radii[1],
Y: r.Rect.Y0 + r.Radii[1],
},
Vec2{
X: r.Radii[1],
Y: r.Radii[1],
},
)
out.LineTo(Pt(
r.Rect.X1,
r.Rect.Y1-r.Radii[2],
))
buildArc(
0,
Point{
X: r.Rect.X1 - r.Radii[2],
Y: r.Rect.Y1 - r.Radii[2],
},
Vec2{
X: r.Radii[2],
Y: r.Radii[2],
},
)
out.LineTo(Pt(
r.Rect.X0+r.Radii[3],
r.Rect.Y1,
))
buildArc(
1,
Point{
X: r.Rect.X0 + r.Radii[3],
Y: r.Rect.Y1 - r.Radii[3],
},
Vec2{
X: r.Radii[3],
Y: r.Radii[3],
},
)
out.ClosePath()
return out
}
func (r RoundedRect) PathLength(accuracy float64) float64 {
corner := func(radius float64) float64 {
return (-2.0 + math.Pi/2) * radius * radius
}
// Start with the full perimeter. For each corner, subtract the
// border surrounding the rounded corner and add the quarter-circle
// perimeter.
return r.Rect.PathLength(1.0) +
corner(r.Radii[0]) +
corner(r.Radii[1]) +
corner(r.Radii[2]) +
corner(r.Radii[3])
}
func (rr RoundedRect) Winding(pt Point) int {
center := rr.Center()
// 1. Translate the point relative to the center of the rectangle.
pt.X -= center.X
pt.Y -= center.Y
// 2. Pick a radius value to use based on which quadrant the point is
// in.
var radius float64
switch {
case pt.X < 0.0 && pt.Y < 0.0:
radius = rr.Radii[0]
case pt.X >= 0.0 && pt.Y < 0.0:
radius = rr.Radii[1]
case pt.X >= 0.0 && pt.Y >= 0.0:
radius = rr.Radii[2]
case pt.X < 0.0 && pt.Y >= 0.0:
radius = rr.Radii[3]
}
// 3. This is the width and height of a rectangle with one corner at
// the center of the rounded rectangle, and another corner at the
// center of the relevant corner circle.
insideHalfWidth := max(rr.Width()/2.0-radius, 0)
insideHalfHeight := max(rr.Height()/2.0-radius, 0)
// 4. Three things are happening here.
//
// First, the x- and y-values are being reflected into the positive
// (bottom-right quadrant). The radius has already been determined,
// so it doesn't matter what quadrant is used.
//
// After reflecting, the points are clamped so that their x- and y-
// values can't be lower than the x- and y- values of the center of
// the corner circle, and the coordinate system is transformed
// again, putting (0, 0) at the center of the corner circle.
px := max(math.Abs(pt.X)-insideHalfWidth, 0.0)
py := max(math.Abs(pt.Y)-insideHalfHeight, 0.0)
// 5. The transforms above clamp all input points such that they will
// be inside the rounded rectangle if the corresponding output point
// (px, py) is inside a circle centered around the origin with the
// given radius.
inside := px*px+py*py <= radius*radius
if inside {
return 1
} else {
return 0
}
}
var _ Shape = RoundedRect{}
func (r RoundedRect) IsInf() bool {
return r.Rect.IsInf() || r.Radii.IsInf()
}
func (r RoundedRect) IsNaN() bool {
return r.Rect.IsNaN() || r.Radii.IsNaN()
}
type RoundedRectRadii [4]float64
func (r RoundedRectRadii) Abs() RoundedRectRadii {
return RoundedRectRadii{
math.Abs(r[0]),
math.Abs(r[1]),
math.Abs(r[2]),
math.Abs(r[3]),
}
}
func (r RoundedRectRadii) Clamp(max float64) RoundedRectRadii {
return RoundedRectRadii{
min(r[0], max),
min(r[1], max),
min(r[2], max),
min(r[3], max),
}
}
func (r RoundedRectRadii) IsInf() bool {
return math.IsInf(r[0], 0) ||
math.IsInf(r[1], 0) ||
math.IsInf(r[2], 0) ||
math.IsInf(r[3], 0)
}
func (r RoundedRectRadii) IsNaN() bool {
return math.IsNaN(r[0]) ||
math.IsNaN(r[1]) ||
math.IsNaN(r[2]) ||
math.IsNaN(r[3])
}