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Source file src/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		"image/color"
     9		"strconv"
    10	)
    11	
    12	// A Point is an X, Y coordinate pair. The axes increase right and down.
    13	type Point struct {
    14		X, Y int
    15	}
    16	
    17	// String returns a string representation of p like "(3,4)".
    18	func (p Point) String() string {
    19		return "(" + strconv.Itoa(p.X) + "," + strconv.Itoa(p.Y) + ")"
    20	}
    21	
    22	// Add returns the vector p+q.
    23	func (p Point) Add(q Point) Point {
    24		return Point{p.X + q.X, p.Y + q.Y}
    25	}
    26	
    27	// Sub returns the vector p-q.
    28	func (p Point) Sub(q Point) Point {
    29		return Point{p.X - q.X, p.Y - q.Y}
    30	}
    31	
    32	// Mul returns the vector p*k.
    33	func (p Point) Mul(k int) Point {
    34		return Point{p.X * k, p.Y * k}
    35	}
    36	
    37	// Div returns the vector p/k.
    38	func (p Point) Div(k int) Point {
    39		return Point{p.X / k, p.Y / k}
    40	}
    41	
    42	// In reports whether p is in r.
    43	func (p Point) In(r Rectangle) bool {
    44		return r.Min.X <= p.X && p.X < r.Max.X &&
    45			r.Min.Y <= p.Y && p.Y < r.Max.Y
    46	}
    47	
    48	// Mod returns the point q in r such that p.X-q.X is a multiple of r's width
    49	// and p.Y-q.Y is a multiple of r's height.
    50	func (p Point) Mod(r Rectangle) Point {
    51		w, h := r.Dx(), r.Dy()
    52		p = p.Sub(r.Min)
    53		p.X = p.X % w
    54		if p.X < 0 {
    55			p.X += w
    56		}
    57		p.Y = p.Y % h
    58		if p.Y < 0 {
    59			p.Y += h
    60		}
    61		return p.Add(r.Min)
    62	}
    63	
    64	// Eq reports whether p and q are equal.
    65	func (p Point) Eq(q Point) bool {
    66		return p == q
    67	}
    68	
    69	// ZP is the zero Point.
    70	var ZP Point
    71	
    72	// Pt is shorthand for Point{X, Y}.
    73	func Pt(X, Y int) Point {
    74		return Point{X, Y}
    75	}
    76	
    77	// A Rectangle contains the points with Min.X <= X < Max.X, Min.Y <= Y < Max.Y.
    78	// It is well-formed if Min.X <= Max.X and likewise for Y. Points are always
    79	// well-formed. A rectangle's methods always return well-formed outputs for
    80	// well-formed inputs.
    81	//
    82	// A Rectangle is also an Image whose bounds are the rectangle itself. At
    83	// returns color.Opaque for points in the rectangle and color.Transparent
    84	// otherwise.
    85	type Rectangle struct {
    86		Min, Max Point
    87	}
    88	
    89	// String returns a string representation of r like "(3,4)-(6,5)".
    90	func (r Rectangle) String() string {
    91		return r.Min.String() + "-" + r.Max.String()
    92	}
    93	
    94	// Dx returns r's width.
    95	func (r Rectangle) Dx() int {
    96		return r.Max.X - r.Min.X
    97	}
    98	
    99	// Dy returns r's height.
   100	func (r Rectangle) Dy() int {
   101		return r.Max.Y - r.Min.Y
   102	}
   103	
   104	// Size returns r's width and height.
   105	func (r Rectangle) Size() Point {
   106		return Point{
   107			r.Max.X - r.Min.X,
   108			r.Max.Y - r.Min.Y,
   109		}
   110	}
   111	
   112	// Add returns the rectangle r translated by p.
   113	func (r Rectangle) Add(p Point) Rectangle {
   114		return Rectangle{
   115			Point{r.Min.X + p.X, r.Min.Y + p.Y},
   116			Point{r.Max.X + p.X, r.Max.Y + p.Y},
   117		}
   118	}
   119	
   120	// Sub returns the rectangle r translated by -p.
   121	func (r Rectangle) Sub(p Point) Rectangle {
   122		return Rectangle{
   123			Point{r.Min.X - p.X, r.Min.Y - p.Y},
   124			Point{r.Max.X - p.X, r.Max.Y - p.Y},
   125		}
   126	}
   127	
   128	// Inset returns the rectangle r inset by n, which may be negative. If either
   129	// of r's dimensions is less than 2*n then an empty rectangle near the center
   130	// of r will be returned.
   131	func (r Rectangle) Inset(n int) Rectangle {
   132		if r.Dx() < 2*n {
   133			r.Min.X = (r.Min.X + r.Max.X) / 2
   134			r.Max.X = r.Min.X
   135		} else {
   136			r.Min.X += n
   137			r.Max.X -= n
   138		}
   139		if r.Dy() < 2*n {
   140			r.Min.Y = (r.Min.Y + r.Max.Y) / 2
   141			r.Max.Y = r.Min.Y
   142		} else {
   143			r.Min.Y += n
   144			r.Max.Y -= n
   145		}
   146		return r
   147	}
   148	
   149	// Intersect returns the largest rectangle contained by both r and s. If the
   150	// two rectangles do not overlap then the zero rectangle will be returned.
   151	func (r Rectangle) Intersect(s Rectangle) Rectangle {
   152		if r.Min.X < s.Min.X {
   153			r.Min.X = s.Min.X
   154		}
   155		if r.Min.Y < s.Min.Y {
   156			r.Min.Y = s.Min.Y
   157		}
   158		if r.Max.X > s.Max.X {
   159			r.Max.X = s.Max.X
   160		}
   161		if r.Max.Y > s.Max.Y {
   162			r.Max.Y = s.Max.Y
   163		}
   164		if r.Min.X > r.Max.X || r.Min.Y > r.Max.Y {
   165			return ZR
   166		}
   167		return r
   168	}
   169	
   170	// Union returns the smallest rectangle that contains both r and s.
   171	func (r Rectangle) Union(s Rectangle) Rectangle {
   172		if r.Empty() {
   173			return s
   174		}
   175		if s.Empty() {
   176			return r
   177		}
   178		if r.Min.X > s.Min.X {
   179			r.Min.X = s.Min.X
   180		}
   181		if r.Min.Y > s.Min.Y {
   182			r.Min.Y = s.Min.Y
   183		}
   184		if r.Max.X < s.Max.X {
   185			r.Max.X = s.Max.X
   186		}
   187		if r.Max.Y < s.Max.Y {
   188			r.Max.Y = s.Max.Y
   189		}
   190		return r
   191	}
   192	
   193	// Empty reports whether the rectangle contains no points.
   194	func (r Rectangle) Empty() bool {
   195		return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
   196	}
   197	
   198	// Eq reports whether r and s contain the same set of points. All empty
   199	// rectangles are considered equal.
   200	func (r Rectangle) Eq(s Rectangle) bool {
   201		return r == s || r.Empty() && s.Empty()
   202	}
   203	
   204	// Overlaps reports whether r and s have a non-empty intersection.
   205	func (r Rectangle) Overlaps(s Rectangle) bool {
   206		return !r.Empty() && !s.Empty() &&
   207			r.Min.X < s.Max.X && s.Min.X < r.Max.X &&
   208			r.Min.Y < s.Max.Y && s.Min.Y < r.Max.Y
   209	}
   210	
   211	// In reports whether every point in r is in s.
   212	func (r Rectangle) In(s Rectangle) bool {
   213		if r.Empty() {
   214			return true
   215		}
   216		// Note that r.Max is an exclusive bound for r, so that r.In(s)
   217		// does not require that r.Max.In(s).
   218		return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
   219			s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
   220	}
   221	
   222	// Canon returns the canonical version of r. The returned rectangle has minimum
   223	// and maximum coordinates swapped if necessary so that it is well-formed.
   224	func (r Rectangle) Canon() Rectangle {
   225		if r.Max.X < r.Min.X {
   226			r.Min.X, r.Max.X = r.Max.X, r.Min.X
   227		}
   228		if r.Max.Y < r.Min.Y {
   229			r.Min.Y, r.Max.Y = r.Max.Y, r.Min.Y
   230		}
   231		return r
   232	}
   233	
   234	// At implements the Image interface.
   235	func (r Rectangle) At(x, y int) color.Color {
   236		if (Point{x, y}).In(r) {
   237			return color.Opaque
   238		}
   239		return color.Transparent
   240	}
   241	
   242	// Bounds implements the Image interface.
   243	func (r Rectangle) Bounds() Rectangle {
   244		return r
   245	}
   246	
   247	// ColorModel implements the Image interface.
   248	func (r Rectangle) ColorModel() color.Model {
   249		return color.Alpha16Model
   250	}
   251	
   252	// ZR is the zero Rectangle.
   253	var ZR Rectangle
   254	
   255	// Rect is shorthand for Rectangle{Pt(x0, y0), Pt(x1, y1)}. The returned
   256	// rectangle has minimum and maximum coordinates swapped if necessary so that
   257	// it is well-formed.
   258	func Rect(x0, y0, x1, y1 int) Rectangle {
   259		if x0 > x1 {
   260			x0, x1 = x1, x0
   261		}
   262		if y0 > y1 {
   263			y0, y1 = y1, y0
   264		}
   265		return Rectangle{Point{x0, y0}, Point{x1, y1}}
   266	}
   267	

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