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| # Code is Public Domain. import math # required because of 'sqrt' in 'distanceTo' function # also tan and atan for rotations. def normalize(x1, y1, x2, y2): '''I am not sure what this is for, care to comment?''' return min(x1,x2), min(y1,y2), max(x1,x2), max(y1,y2) |
"""Point and Rectangle classes. This code is in the public domain. Point -- point with (x,y) coordinates Rect -- two points, forming a rectangle """ import math |
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"""A point identified by (x,y) coordinates. supports: +, -, *, /, str, repr as_tuple -- construct tuple (x,y) clone -- construct a duplicate integerize -- convert x & y to integers floatize -- convert x & y to floats distance_to -- calculate distance between points move_to -- reset x & y slide -- move to +dx, +dy rotate -- rotate around the origin rotate_about -- rotate around another point """ |
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| """Point(x1+x2, y1+y2)""" | |
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| """Point(x1-x2, y1-y2)""" | |
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| """Point(x1*x2, y1*y2)""" | |
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| """Point(x1/x2, y1/y2)""" | |
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| def XY(self): '''Returns a tuple (x,y).''' return self.x,self.y def Clone(self): '''Returns a full copy of this point.''' |
def as_tuple(self): """(x, y)""" return (self.x, self.y) def clone(self): """Return a full copy of this point.""" |
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| def Integerize(self): '''Rounds co-ordinate values to integers.''' |
def integerize(self): """Convert co-ordinate values to integers.""" |
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| def Floatize(self): '''Converts co-ordinate values to floating point (is this necessary?)''' |
def floatize(self): """Convert co-ordinate values to floats.""" |
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| def DistanceTo(self,pt): '''Distance between 2 points.''' dy = self.y - pt.y dx = self.x - pt.x |
def distance_to(self, pt): """Calculate the distance between two points.""" dy = float(self.y - pt.y) dx = float(self.x - pt.x) |
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| def Move(newx,newy): '''Changes coordinates to those given.''' self.x = newx self.y = newy def MoveDelta(dx,dy): '''Move to new (x+dx,y+dy)''' |
def move_to(self, x, y): """Reset x & y coordinates.""" self.x = x self.y = y def slide(self, dx, dy): '''Move to new (x+dx,y+dy). Can anyone think up a better name for this function? slide? shift? delta? move_by? ''' |
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| def Rotate(self,theta): '''Clockwise rotation about origin, theta in Degrees. Returns the new position as Point()''' # Err..this math is not exactly readable. # It is elementary though, involving only Pythogoras and basic trig. r2 = sqr(self.x)+sqr(self.y) |
def rotate(self, theta): """Rotate clockwise by theta degrees. Rotate the point clockwise, around the origin. The new position is returned as a new Point. WARNING: UNTESTED CODE. """ r2 = math.sqrt(self.x)+math.sqrt(self.y) |
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| ret = Point() ret.x = math.sqrt(r2/(1+tmp*tmp)) ret.y = ret.x * tmp return ret def RotateAbout(self,OtherPoint,theta): '''Clockwise rotation about another point. Returns a Point() at new position''' tmpx = OtherPoint.x tmpy = OtherPoint.y self.MoveDelta(-tmpx,-tmpy) tmpPoint = self.Rotate(theta) tmpPoint.MoveDelta(tmpx,tmpy) return tmpPoint |
return Point(math.sqrt(r2/(1+tmp*tmp)), ret.x * tmp) def rotate_about(self, pt, theta): """Rotate clockwise around a point, by theta degrees. Rotate the point clockwise, around another point. The new position is returned as a new Point. WARNING: UNTESTED CODE. """ result = self.clone() result.slide(-pt.x, -pt.y) result.rotate(theta) result.slide(pt.x, pt.y) return result |
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"""A rectangle identified by two points. The rectangle stores left, top, right, and bottom values. Coordinates are based on screen coordinates. origin top +-----> x increases | | left -+- right v | y increases bottom set_points -- reset rectangle coordinates contains -- is a point inside? overlaps -- does a rectangle overlap? top_left -- get top-left corner bottom_right -- get bottom-right corner expanded_by -- grow (or shrink) """ |
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| self.Set(pt1, pt2) def Contains(self, pt): x,y = pt.XY() return self.left <= x <= self.right and self.top <= y <= self.bottom def Set( self, pt1, pt2 ): extrema = normalize(pt1.x, pt1.y, pt2.x, pt2.y) self.left, self.top, self.right, self.bottom = extrema def Overlaps(self, other): return (self.right > other.left and self.left < other.right and self.top < other.bottom and self.bottom > other.top) def GetTL(self): |
"""Initialize a rectangle from two points.""" self.set_points(pt1, pt2) def set_points(self, pt1, pt2): """Reset the rectangle coordinates.""" (x1, y1) = pt1.as_tuple() (x2, y2) = pt2.as_tuple() self.left = min(x1, x2) self.top = min(y1, y2) self.right = max(x1, x2) self.bottom = max(y1, y2) def contains(self, pt): """Return true if a point is inside the rectangle.""" x,y = pt.as_tuple() return (self.left <= x <= self.right and self.top <= y <= self.bottom) def overlaps(self, other): """Return true if a rectangle overlaps this rectangle.""" return (self.right > other.left and self.left < other.right and self.top < other.bottom and self.bottom > other.top) def top_left(self): """Return the top-left corner as a Point.""" |
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| def GetBR(self): | def bottom_right(self): """Return the bottom-right corner as a Point.""" |
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| def ExpandedBy(self, n): p1 = Point(self.left-n, self.top+n) |
def expanded_by(self, n): """Return a rectangle with extended borders. Create a new rectangle that is wider and taller than the immediate one. All sides are extended by "n" points. """ p1 = Point(self.left-n, self.top-n) |
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| def TransformedByFunction(self, foo): p1 = Point(self.left, self.top) p2 = Point(self.right, self.bottom) return Rect(foo(p1), foo(p2)) |
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== See Also == * [http://en.wikipedia.org/wiki/Cartesian_coordinate_system Wikipedia:Cartesian coordinate system] * [http://en.wikipedia.org/wiki/Vector_%28spatial%29 Wikipedia:Vector] |
Points & Rectangles
A pair of classes to provide points and rectangles.
Surprisingly, I haven't been able to find a single Python module providing such primitive support.
WxPython supports wxPoint and wxRect, but it lacks many basic functions (such as, say, adding two points together to produce a third point..!)
This code is lacking a zillion essential features (but interpoint distance can now be calculated). I only put in the ones I needed immediately. Please add, refactor, optimize, rename stuff to be more standard, etc., as you see fit..!
If there's an actual, accessible, easy-to-include Python module, not tied to a graphics library, that does this stuff already, please write about it here! No sense in reinventing the wheel. I've looked, but haven't found one. Hence this.
1 """Point and Rectangle classes.
2
3 This code is in the public domain.
4
5 Point -- point with (x,y) coordinates
6 Rect -- two points, forming a rectangle
7 """
8
9 import math
10
11
12 class Point:
13
14 """A point identified by (x,y) coordinates.
15
16 supports: +, -, *, /, str, repr
17
18 as_tuple -- construct tuple (x,y)
19 clone -- construct a duplicate
20 integerize -- convert x & y to integers
21 floatize -- convert x & y to floats
22 distance_to -- calculate distance between points
23 move_to -- reset x & y
24 slide -- move to +dx, +dy
25 rotate -- rotate around the origin
26 rotate_about -- rotate around another point
27 """
28
29 def __init__(self, x, y):
30 self.x = x
31 self.y = y
32
33 def __add__(self, other):
34 """Point(x1+x2, y1+y2)"""
35 return Point(self.x+other.x, self.y+other.y)
36
37 def __sub__(self, other):
38 """Point(x1-x2, y1-y2)"""
39 return Point(self.x-other.x, self.y-other.y)
40
41 def __mul__( self, scalar ):
42 """Point(x1*x2, y1*y2)"""
43 return Point(self.x*scalar, self.y*scalar)
44
45 def __div__(self, scalar):
46 """Point(x1/x2, y1/y2)"""
47 return Point(self.x/scalar, self.y/scalar)
48
49 def __str__(self):
50 return "(%s, %s)" % (self.x, self.y)
51
52 def __repr__(self):
53 return "%s(%r, %r)" % (self.__class__.__name__, self.x, self.y)
54
55 def as_tuple(self):
56 """(x, y)"""
57 return (self.x, self.y)
58
59 def clone(self):
60 """Return a full copy of this point."""
61 return Point(self.x, self.y)
62
63 def integerize(self):
64 """Convert co-ordinate values to integers."""
65 self.x = int(self.x)
66 self.y = int(self.y)
67
68 def floatize(self):
69 """Convert co-ordinate values to floats."""
70 self.x = float(self.x)
71 self.y = float(self.y)
72
73 def distance_to(self, pt):
74 """Calculate the distance between two points."""
75 dy = float(self.y - pt.y)
76 dx = float(self.x - pt.x)
77 return sqrt(dy*dy + dx*dx)
78
79 def move_to(self, x, y):
80 """Reset x & y coordinates."""
81 self.x = x
82 self.y = y
83
84 def slide(self, dx, dy):
85 '''Move to new (x+dx,y+dy).
86
87 Can anyone think up a better name for this function?
88 slide? shift? delta? move_by?
89 '''
90 self.x = self.x + dx
91 self.y = self.y + dy
92
93 def rotate(self, theta):
94 """Rotate clockwise by theta degrees.
95
96 Rotate the point clockwise, around the origin.
97 The new position is returned as a new Point.
98
99 WARNING: UNTESTED CODE.
100 """
101 r2 = math.sqrt(self.x)+math.sqrt(self.y)
102 tmp = math.tan(theta*math.pi/90 + math.atan(self.x/self.y))
103 return Point(math.sqrt(r2/(1+tmp*tmp)),
104 ret.x * tmp)
105
106 def rotate_about(self, pt, theta):
107 """Rotate clockwise around a point, by theta degrees.
108
109 Rotate the point clockwise, around another point.
110 The new position is returned as a new Point.
111
112 WARNING: UNTESTED CODE.
113 """
114 result = self.clone()
115 result.slide(-pt.x, -pt.y)
116 result.rotate(theta)
117 result.slide(pt.x, pt.y)
118 return result
119
120
121 class Rect:
122
123 """A rectangle identified by two points.
124
125 The rectangle stores left, top, right, and bottom values.
126
127 Coordinates are based on screen coordinates.
128
129 origin top
130 +-----> x increases |
131 | left -+- right
132 v |
133 y increases bottom
134
135 set_points -- reset rectangle coordinates
136 contains -- is a point inside?
137 overlaps -- does a rectangle overlap?
138 top_left -- get top-left corner
139 bottom_right -- get bottom-right corner
140 expanded_by -- grow (or shrink)
141 """
142
143 def __init__(self, pt1, pt2):
144 """Initialize a rectangle from two points."""
145 self.set_points(pt1, pt2)
146
147 def set_points(self, pt1, pt2):
148 """Reset the rectangle coordinates."""
149 (x1, y1) = pt1.as_tuple()
150 (x2, y2) = pt2.as_tuple()
151 self.left = min(x1, x2)
152 self.top = min(y1, y2)
153 self.right = max(x1, x2)
154 self.bottom = max(y1, y2)
155
156 def contains(self, pt):
157 """Return true if a point is inside the rectangle."""
158 x,y = pt.as_tuple()
159 return (self.left <= x <= self.right and
160 self.top <= y <= self.bottom)
161
162 def overlaps(self, other):
163 """Return true if a rectangle overlaps this rectangle."""
164 return (self.right > other.left and self.left < other.right and
165 self.top < other.bottom and self.bottom > other.top)
166
167 def top_left(self):
168 """Return the top-left corner as a Point."""
169 return Point(self.left, self.top)
170
171 def bottom_right(self):
172 """Return the bottom-right corner as a Point."""
173 return Point(self.right, self.bottom)
174
175 def expanded_by(self, n):
176 """Return a rectangle with extended borders.
177
178 Create a new rectangle that is wider and taller than the
179 immediate one. All sides are extended by "n" points.
180 """
181 p1 = Point(self.left-n, self.top-n)
182 p2 = Point(self.right+n, self.bottom+n)
183 return Rect(p1, p2)
184
185 def __str__( self ):
186 return "<Rect (%s,%s)-(%s,%s)>" % (self.left,self.top,
187 self.right,self.bottom)
188
189 def __repr__(self):
190 return "%s(%r, %r)" % (self.__class__.__name__,
191 Point(self.left, self.top),
192 Point(self.right, self.bottom))
See Also
[http://en.wikipedia.org/wiki/Cartesian_coordinate_system Wikipedia:Cartesian coordinate system]
[http://en.wikipedia.org/wiki/Vector_%28spatial%29 Wikipedia:Vector]