gtsocial-umbx

rect.go (8252B)

---

 // Copyright 2014 Google Inc. All rights reserved.
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
 // You may obtain a copy of the License at
 //
 //     http://www.apache.org/licenses/LICENSE-2.0
 //
 // Unless required by applicable law or agreed to in writing, software
 // distributed under the License is distributed on an "AS IS" BASIS,
 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
 package r2
 
 import (
 	"fmt"
 	"math"
 
 	"github.com/golang/geo/r1"
 )
 
 // Point represents a point in ℝ².
 type Point struct {
 	X, Y float64
 }
 
 // Add returns the sum of p and op.
 func (p Point) Add(op Point) Point { return Point{p.X + op.X, p.Y + op.Y} }
 
 // Sub returns the difference of p and op.
 func (p Point) Sub(op Point) Point { return Point{p.X - op.X, p.Y - op.Y} }
 
 // Mul returns the scalar product of p and m.
 func (p Point) Mul(m float64) Point { return Point{m * p.X, m * p.Y} }
 
 // Ortho returns a counterclockwise orthogonal point with the same norm.
 func (p Point) Ortho() Point { return Point{-p.Y, p.X} }
 
 // Dot returns the dot product between p and op.
 func (p Point) Dot(op Point) float64 { return p.X*op.X + p.Y*op.Y }
 
 // Cross returns the cross product of p and op.
 func (p Point) Cross(op Point) float64 { return p.X*op.Y - p.Y*op.X }
 
 // Norm returns the vector's norm.
 func (p Point) Norm() float64 { return math.Hypot(p.X, p.Y) }
 
 // Normalize returns a unit point in the same direction as p.
 func (p Point) Normalize() Point {
 	if p.X == 0 && p.Y == 0 {
 		return p
 	}
 	return p.Mul(1 / p.Norm())
 }
 
 func (p Point) String() string { return fmt.Sprintf("(%.12f, %.12f)", p.X, p.Y) }
 
 // Rect represents a closed axis-aligned rectangle in the (x,y) plane.
 type Rect struct {
 	X, Y r1.Interval
 }
 
 // RectFromPoints constructs a rect that contains the given points.
 func RectFromPoints(pts ...Point) Rect {
 	// Because the default value on interval is 0,0, we need to manually
 	// define the interval from the first point passed in as our starting
 	// interval, otherwise we end up with the case of passing in
 	// Point{0.2, 0.3} and getting the starting Rect of {0, 0.2}, {0, 0.3}
 	// instead of the Rect {0.2, 0.2}, {0.3, 0.3} which is not correct.
 	if len(pts) == 0 {
 		return Rect{}
 	}
 
 	r := Rect{
 		X: r1.Interval{Lo: pts[0].X, Hi: pts[0].X},
 		Y: r1.Interval{Lo: pts[0].Y, Hi: pts[0].Y},
 	}
 
 	for _, p := range pts[1:] {
 		r = r.AddPoint(p)
 	}
 	return r
 }
 
 // RectFromCenterSize constructs a rectangle with the given center and size.
 // Both dimensions of size must be non-negative.
 func RectFromCenterSize(center, size Point) Rect {
 	return Rect{
 		r1.Interval{Lo: center.X - size.X/2, Hi: center.X + size.X/2},
 		r1.Interval{Lo: center.Y - size.Y/2, Hi: center.Y + size.Y/2},
 	}
 }
 
 // EmptyRect constructs the canonical empty rectangle. Use IsEmpty() to test
 // for empty rectangles, since they have more than one representation. A Rect{}
 // is not the same as the EmptyRect.
 func EmptyRect() Rect {
 	return Rect{r1.EmptyInterval(), r1.EmptyInterval()}
 }
 
 // IsValid reports whether the rectangle is valid.
 // This requires the width to be empty iff the height is empty.
 func (r Rect) IsValid() bool {
 	return r.X.IsEmpty() == r.Y.IsEmpty()
 }
 
 // IsEmpty reports whether the rectangle is empty.
 func (r Rect) IsEmpty() bool {
 	return r.X.IsEmpty()
 }
 
 // Vertices returns all four vertices of the rectangle. Vertices are returned in
 // CCW direction starting with the lower left corner.
 func (r Rect) Vertices() [4]Point {
 	return [4]Point{
 		{r.X.Lo, r.Y.Lo},
 		{r.X.Hi, r.Y.Lo},
 		{r.X.Hi, r.Y.Hi},
 		{r.X.Lo, r.Y.Hi},
 	}
 }
 
 // VertexIJ returns the vertex in direction i along the X-axis (0=left, 1=right) and
 // direction j along the Y-axis (0=down, 1=up).
 func (r Rect) VertexIJ(i, j int) Point {
 	x := r.X.Lo
 	if i == 1 {
 		x = r.X.Hi
 	}
 	y := r.Y.Lo
 	if j == 1 {
 		y = r.Y.Hi
 	}
 	return Point{x, y}
 }
 
 // Lo returns the low corner of the rect.
 func (r Rect) Lo() Point {
 	return Point{r.X.Lo, r.Y.Lo}
 }
 
 // Hi returns the high corner of the rect.
 func (r Rect) Hi() Point {
 	return Point{r.X.Hi, r.Y.Hi}
 }
 
 // Center returns the center of the rectangle in (x,y)-space
 func (r Rect) Center() Point {
 	return Point{r.X.Center(), r.Y.Center()}
 }
 
 // Size returns the width and height of this rectangle in (x,y)-space. Empty
 // rectangles have a negative width and height.
 func (r Rect) Size() Point {
 	return Point{r.X.Length(), r.Y.Length()}
 }
 
 // ContainsPoint reports whether the rectangle contains the given point.
 // Rectangles are closed regions, i.e. they contain their boundary.
 func (r Rect) ContainsPoint(p Point) bool {
 	return r.X.Contains(p.X) && r.Y.Contains(p.Y)
 }
 
 // InteriorContainsPoint returns true iff the given point is contained in the interior
 // of the region (i.e. the region excluding its boundary).
 func (r Rect) InteriorContainsPoint(p Point) bool {
 	return r.X.InteriorContains(p.X) && r.Y.InteriorContains(p.Y)
 }
 
 // Contains reports whether the rectangle contains the given rectangle.
 func (r Rect) Contains(other Rect) bool {
 	return r.X.ContainsInterval(other.X) && r.Y.ContainsInterval(other.Y)
 }
 
 // InteriorContains reports whether the interior of this rectangle contains all of the
 // points of the given other rectangle (including its boundary).
 func (r Rect) InteriorContains(other Rect) bool {
 	return r.X.InteriorContainsInterval(other.X) && r.Y.InteriorContainsInterval(other.Y)
 }
 
 // Intersects reports whether this rectangle and the other rectangle have any points in common.
 func (r Rect) Intersects(other Rect) bool {
 	return r.X.Intersects(other.X) && r.Y.Intersects(other.Y)
 }
 
 // InteriorIntersects reports whether the interior of this rectangle intersects
 // any point (including the boundary) of the given other rectangle.
 func (r Rect) InteriorIntersects(other Rect) bool {
 	return r.X.InteriorIntersects(other.X) && r.Y.InteriorIntersects(other.Y)
 }
 
 // AddPoint expands the rectangle to include the given point. The rectangle is
 // expanded by the minimum amount possible.
 func (r Rect) AddPoint(p Point) Rect {
 	return Rect{r.X.AddPoint(p.X), r.Y.AddPoint(p.Y)}
 }
 
 // AddRect expands the rectangle to include the given rectangle. This is the
 // same as replacing the rectangle by the union of the two rectangles, but
 // is more efficient.
 func (r Rect) AddRect(other Rect) Rect {
 	return Rect{r.X.Union(other.X), r.Y.Union(other.Y)}
 }
 
 // ClampPoint returns the closest point in the rectangle to the given point.
 // The rectangle must be non-empty.
 func (r Rect) ClampPoint(p Point) Point {
 	return Point{r.X.ClampPoint(p.X), r.Y.ClampPoint(p.Y)}
 }
 
 // Expanded returns a rectangle that has been expanded in the x-direction
 // by margin.X, and in y-direction by margin.Y. If either margin is empty,
 // then shrink the interval on the corresponding sides instead. The resulting
 // rectangle may be empty. Any expansion of an empty rectangle remains empty.
 func (r Rect) Expanded(margin Point) Rect {
 	xx := r.X.Expanded(margin.X)
 	yy := r.Y.Expanded(margin.Y)
 	if xx.IsEmpty() || yy.IsEmpty() {
 		return EmptyRect()
 	}
 	return Rect{xx, yy}
 }
 
 // ExpandedByMargin returns a Rect that has been expanded by the amount on all sides.
 func (r Rect) ExpandedByMargin(margin float64) Rect {
 	return r.Expanded(Point{margin, margin})
 }
 
 // Union returns the smallest rectangle containing the union of this rectangle and
 // the given rectangle.
 func (r Rect) Union(other Rect) Rect {
 	return Rect{r.X.Union(other.X), r.Y.Union(other.Y)}
 }
 
 // Intersection returns the smallest rectangle containing the intersection of this
 // rectangle and the given rectangle.
 func (r Rect) Intersection(other Rect) Rect {
 	xx := r.X.Intersection(other.X)
 	yy := r.Y.Intersection(other.Y)
 	if xx.IsEmpty() || yy.IsEmpty() {
 		return EmptyRect()
 	}
 
 	return Rect{xx, yy}
 }
 
 // ApproxEqual returns true if the x- and y-intervals of the two rectangles are
 // the same up to the given tolerance.
 func (r Rect) ApproxEqual(r2 Rect) bool {
 	return r.X.ApproxEqual(r2.X) && r.Y.ApproxEqual(r2.Y)
 }
 
 func (r Rect) String() string { return fmt.Sprintf("[Lo%s, Hi%s]", r.Lo(), r.Hi()) }