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Source file src/image/geom.go

Documentation: image

     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  	// Letting r0 and s0 be the values of r and s at the time that the method
   165  	// is called, this next line is equivalent to:
   166  	//
   167  	// if max(r0.Min.X, s0.Min.X) >= min(r0.Max.X, s0.Max.X) || likewiseForY { etc }
   168  	if r.Empty() {
   169  		return ZR
   170  	}
   171  	return r
   172  }
   173  
   174  // Union returns the smallest rectangle that contains both r and s.
   175  func (r Rectangle) Union(s Rectangle) Rectangle {
   176  	if r.Empty() {
   177  		return s
   178  	}
   179  	if s.Empty() {
   180  		return r
   181  	}
   182  	if r.Min.X > s.Min.X {
   183  		r.Min.X = s.Min.X
   184  	}
   185  	if r.Min.Y > s.Min.Y {
   186  		r.Min.Y = s.Min.Y
   187  	}
   188  	if r.Max.X < s.Max.X {
   189  		r.Max.X = s.Max.X
   190  	}
   191  	if r.Max.Y < s.Max.Y {
   192  		r.Max.Y = s.Max.Y
   193  	}
   194  	return r
   195  }
   196  
   197  // Empty reports whether the rectangle contains no points.
   198  func (r Rectangle) Empty() bool {
   199  	return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
   200  }
   201  
   202  // Eq reports whether r and s contain the same set of points. All empty
   203  // rectangles are considered equal.
   204  func (r Rectangle) Eq(s Rectangle) bool {
   205  	return r == s || r.Empty() && s.Empty()
   206  }
   207  
   208  // Overlaps reports whether r and s have a non-empty intersection.
   209  func (r Rectangle) Overlaps(s Rectangle) bool {
   210  	return !r.Empty() && !s.Empty() &&
   211  		r.Min.X < s.Max.X && s.Min.X < r.Max.X &&
   212  		r.Min.Y < s.Max.Y && s.Min.Y < r.Max.Y
   213  }
   214  
   215  // In reports whether every point in r is in s.
   216  func (r Rectangle) In(s Rectangle) bool {
   217  	if r.Empty() {
   218  		return true
   219  	}
   220  	// Note that r.Max is an exclusive bound for r, so that r.In(s)
   221  	// does not require that r.Max.In(s).
   222  	return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
   223  		s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
   224  }
   225  
   226  // Canon returns the canonical version of r. The returned rectangle has minimum
   227  // and maximum coordinates swapped if necessary so that it is well-formed.
   228  func (r Rectangle) Canon() Rectangle {
   229  	if r.Max.X < r.Min.X {
   230  		r.Min.X, r.Max.X = r.Max.X, r.Min.X
   231  	}
   232  	if r.Max.Y < r.Min.Y {
   233  		r.Min.Y, r.Max.Y = r.Max.Y, r.Min.Y
   234  	}
   235  	return r
   236  }
   237  
   238  // At implements the Image interface.
   239  func (r Rectangle) At(x, y int) color.Color {
   240  	if (Point{x, y}).In(r) {
   241  		return color.Opaque
   242  	}
   243  	return color.Transparent
   244  }
   245  
   246  // Bounds implements the Image interface.
   247  func (r Rectangle) Bounds() Rectangle {
   248  	return r
   249  }
   250  
   251  // ColorModel implements the Image interface.
   252  func (r Rectangle) ColorModel() color.Model {
   253  	return color.Alpha16Model
   254  }
   255  
   256  // ZR is the zero Rectangle.
   257  var ZR Rectangle
   258  
   259  // Rect is shorthand for Rectangle{Pt(x0, y0), Pt(x1, y1)}. The returned
   260  // rectangle has minimum and maximum coordinates swapped if necessary so that
   261  // it is well-formed.
   262  func Rect(x0, y0, x1, y1 int) Rectangle {
   263  	if x0 > x1 {
   264  		x0, x1 = x1, x0
   265  	}
   266  	if y0 > y1 {
   267  		y0, y1 = y1, y0
   268  	}
   269  	return Rectangle{Point{x0, y0}, Point{x1, y1}}
   270  }
   271  

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