Source file src/pkg/image/geom.go

     1	// Copyright 2010 The Go Authors. All rights reserved.
     2	// Use of this source code is governed by a BSD-style
     3	// license that can be found in the LICENSE file.
     4	
     5	package image
     6	
     7	import (
     8		"strconv"
     9	)
    10	
    11	// A Point is an X, Y coordinate pair. The axes increase right and down.
    12	type Point struct {
    13		X, Y int
    14	}
    15	
    16	// String returns a string representation of p like "(3,4)".
    17	func (p Point) String() string {
    18		return "(" + strconv.Itoa(p.X) + "," + strconv.Itoa(p.Y) + ")"
    19	}
    20	
    21	// Add returns the vector p+q.
    22	func (p Point) Add(q Point) Point {
    23		return Point{p.X + q.X, p.Y + q.Y}
    24	}
    25	
    26	// Sub returns the vector p-q.
    27	func (p Point) Sub(q Point) Point {
    28		return Point{p.X - q.X, p.Y - q.Y}
    29	}
    30	
    31	// Mul returns the vector p*k.
    32	func (p Point) Mul(k int) Point {
    33		return Point{p.X * k, p.Y * k}
    34	}
    35	
    36	// Div returns the vector p/k.
    37	func (p Point) Div(k int) Point {
    38		return Point{p.X / k, p.Y / k}
    39	}
    40	
    41	// In returns whether p is in r.
    42	func (p Point) In(r Rectangle) bool {
    43		return r.Min.X <= p.X && p.X < r.Max.X &&
    44			r.Min.Y <= p.Y && p.Y < r.Max.Y
    45	}
    46	
    47	// Mod returns the point q in r such that p.X-q.X is a multiple of r's width
    48	// and p.Y-q.Y is a multiple of r's height.
    49	func (p Point) Mod(r Rectangle) Point {
    50		w, h := r.Dx(), r.Dy()
    51		p = p.Sub(r.Min)
    52		p.X = p.X % w
    53		if p.X < 0 {
    54			p.X += w
    55		}
    56		p.Y = p.Y % h
    57		if p.Y < 0 {
    58			p.Y += h
    59		}
    60		return p.Add(r.Min)
    61	}
    62	
    63	// Eq returns whether p and q are equal.
    64	func (p Point) Eq(q Point) bool {
    65		return p.X == q.X && p.Y == q.Y
    66	}
    67	
    68	// ZP is the zero Point.
    69	var ZP Point
    70	
    71	// Pt is shorthand for Point{X, Y}.
    72	func Pt(X, Y int) Point {
    73		return Point{X, Y}
    74	}
    75	
    76	// A Rectangle contains the points with Min.X <= X < Max.X, Min.Y <= Y < Max.Y.
    77	// It is well-formed if Min.X <= Max.X and likewise for Y. Points are always
    78	// well-formed. A rectangle's methods always return well-formed outputs for
    79	// well-formed inputs.
    80	type Rectangle struct {
    81		Min, Max Point
    82	}
    83	
    84	// String returns a string representation of r like "(3,4)-(6,5)".
    85	func (r Rectangle) String() string {
    86		return r.Min.String() + "-" + r.Max.String()
    87	}
    88	
    89	// Dx returns r's width.
    90	func (r Rectangle) Dx() int {
    91		return r.Max.X - r.Min.X
    92	}
    93	
    94	// Dy returns r's height.
    95	func (r Rectangle) Dy() int {
    96		return r.Max.Y - r.Min.Y
    97	}
    98	
    99	// Size returns r's width and height.
   100	func (r Rectangle) Size() Point {
   101		return Point{
   102			r.Max.X - r.Min.X,
   103			r.Max.Y - r.Min.Y,
   104		}
   105	}
   106	
   107	// Add returns the rectangle r translated by p.
   108	func (r Rectangle) Add(p Point) Rectangle {
   109		return Rectangle{
   110			Point{r.Min.X + p.X, r.Min.Y + p.Y},
   111			Point{r.Max.X + p.X, r.Max.Y + p.Y},
   112		}
   113	}
   114	
   115	// Sub returns the rectangle r translated by -p.
   116	func (r Rectangle) Sub(p Point) Rectangle {
   117		return Rectangle{
   118			Point{r.Min.X - p.X, r.Min.Y - p.Y},
   119			Point{r.Max.X - p.X, r.Max.Y - p.Y},
   120		}
   121	}
   122	
   123	// Inset returns the rectangle r inset by n, which may be negative. If either
   124	// of r's dimensions is less than 2*n then an empty rectangle near the center
   125	// of r will be returned.
   126	func (r Rectangle) Inset(n int) Rectangle {
   127		if r.Dx() < 2*n {
   128			r.Min.X = (r.Min.X + r.Max.X) / 2
   129			r.Max.X = r.Min.X
   130		} else {
   131			r.Min.X += n
   132			r.Max.X -= n
   133		}
   134		if r.Dy() < 2*n {
   135			r.Min.Y = (r.Min.Y + r.Max.Y) / 2
   136			r.Max.Y = r.Min.Y
   137		} else {
   138			r.Min.Y += n
   139			r.Max.Y -= n
   140		}
   141		return r
   142	}
   143	
   144	// Intersect returns the largest rectangle contained by both r and s. If the
   145	// two rectangles do not overlap then the zero rectangle will be returned.
   146	func (r Rectangle) Intersect(s Rectangle) Rectangle {
   147		if r.Min.X < s.Min.X {
   148			r.Min.X = s.Min.X
   149		}
   150		if r.Min.Y < s.Min.Y {
   151			r.Min.Y = s.Min.Y
   152		}
   153		if r.Max.X > s.Max.X {
   154			r.Max.X = s.Max.X
   155		}
   156		if r.Max.Y > s.Max.Y {
   157			r.Max.Y = s.Max.Y
   158		}
   159		if r.Min.X > r.Max.X || r.Min.Y > r.Max.Y {
   160			return ZR
   161		}
   162		return r
   163	}
   164	
   165	// Union returns the smallest rectangle that contains both r and s.
   166	func (r Rectangle) Union(s Rectangle) Rectangle {
   167		if r.Min.X > s.Min.X {
   168			r.Min.X = s.Min.X
   169		}
   170		if r.Min.Y > s.Min.Y {
   171			r.Min.Y = s.Min.Y
   172		}
   173		if r.Max.X < s.Max.X {
   174			r.Max.X = s.Max.X
   175		}
   176		if r.Max.Y < s.Max.Y {
   177			r.Max.Y = s.Max.Y
   178		}
   179		return r
   180	}
   181	
   182	// Empty returns whether the rectangle contains no points.
   183	func (r Rectangle) Empty() bool {
   184		return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
   185	}
   186	
   187	// Eq returns whether r and s are equal.
   188	func (r Rectangle) Eq(s Rectangle) bool {
   189		return r.Min.X == s.Min.X && r.Min.Y == s.Min.Y &&
   190			r.Max.X == s.Max.X && r.Max.Y == s.Max.Y
   191	}
   192	
   193	// Overlaps returns whether r and s have a non-empty intersection.
   194	func (r Rectangle) Overlaps(s Rectangle) bool {
   195		return r.Min.X < s.Max.X && s.Min.X < r.Max.X &&
   196			r.Min.Y < s.Max.Y && s.Min.Y < r.Max.Y
   197	}
   198	
   199	// In returns whether every point in r is in s.
   200	func (r Rectangle) In(s Rectangle) bool {
   201		if r.Empty() {
   202			return true
   203		}
   204		// Note that r.Max is an exclusive bound for r, so that r.In(s)
   205		// does not require that r.Max.In(s).
   206		return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
   207			s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
   208	}
   209	
   210	// Canon returns the canonical version of r. The returned rectangle has minimum
   211	// and maximum coordinates swapped if necessary so that it is well-formed.
   212	func (r Rectangle) Canon() Rectangle {
   213		if r.Max.X < r.Min.X {
   214			r.Min.X, r.Max.X = r.Max.X, r.Min.X
   215		}
   216		if r.Max.Y < r.Min.Y {
   217			r.Min.Y, r.Max.Y = r.Max.Y, r.Min.Y
   218		}
   219		return r
   220	}
   221	
   222	// ZR is the zero Rectangle.
   223	var ZR Rectangle
   224	
   225	// Rect is shorthand for Rectangle{Pt(x0, y0), Pt(x1, y1)}.
   226	func Rect(x0, y0, x1, y1 int) Rectangle {
   227		if x0 > x1 {
   228			x0, x1 = x1, x0
   229		}
   230		if y0 > y1 {
   231			y0, y1 = y1, y0
   232		}
   233		return Rectangle{Point{x0, y0}, Point{x1, y1}}
   234	}