Web   ·   Wiki   ·   Activities   ·   Blog   ·   Lists   ·   Chat   ·   Meeting   ·   Bugs   ·   Git   ·   Translate   ·   Archive   ·   People   ·   Donate
summaryrefslogtreecommitdiffstats
path: root/helpers.py
blob: bc39eb4dffd59ae5ef0cac486751b75f2b085251 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
#==================================================================
#                           Physics.activity
#                     Helper classes and functions
#                           By Alex Levenson
#==================================================================
import math
# distance calculator, pt1 and pt2 are ordred pairs
def distance(pt1, pt2):
        return math.sqrt((pt1[0] - pt2[0]) ** 2 + (pt1[1] -pt2[1]) ** 2)

# returns the angle between the line segment from pt1 --> pt2 and the x axis, from -pi to pi
def getAngle(pt1,pt2):
    xcomp = pt2[0] - pt1[0]
    ycomp = pt1[1] - pt2[1]
    return math.atan2(ycomp,xcomp)

# returns a list of ordered pairs that describe an equilteral triangle around the segment from pt1 --> pt2
def constructTriangleFromLine(p1,p2):
    halfHeightVector = (0.57735*(p2[1] - p1[1]), 0.57735*(p2[0] - p1[0]))
    p3 = (p1[0] + halfHeightVector[0], p1[1] - halfHeightVector[1])
    p4 = (p1[0] - halfHeightVector[0], p1[1] + halfHeightVector[1])
    return [p2,p3,p4]

# returns the area of a polygon
def polyArea(vertices):
    n = len(vertices)
    A = 0
    p=n-1
    q=0
    while q<n:
        A+=vertices[p][0]*vertices[q][1] - vertices[q][0]*vertices[p][1]
        p=q
        q += 1
    return A/2.0

#Some polygon magic, thanks to John W. Ratcliff on www.flipcode.com
    
# returns true if pt is in triangle
def insideTriangle(pt,triangle):

    ax = triangle[2][0] - triangle[1][0]
    ay = triangle[2][1] - triangle[1][1]
    bx = triangle[0][0] - triangle[2][0]
    by = triangle[0][1] - triangle[2][1]
    cx = triangle[1][0] - triangle[0][0]
    cy = triangle[1][1] - triangle[0][1]
    apx= pt[0] - triangle[0][0]
    apy= pt[1] - triangle[0][1]
    bpx= pt[0] - triangle[1][0]
    bpy= pt[1] - triangle[1][1]
    cpx= pt[0] - triangle[2][0]
    cpy= pt[1] - triangle[2][1]
    
    aCROSSbp = ax*bpy - ay*bpx
    cCROSSap = cx*apy - cy*apx
    bCROSScp = bx*cpy - by*cpx  
    return aCROSSbp >= 0.0 and bCROSScp >= 0.0 and cCROSSap >= 0.0    

def polySnip(vertices,u,v,w,n):
    EPSILON = 0.0000000001
    
    Ax = vertices[u][0]
    Ay = vertices[u][1]
    
    Bx = vertices[v][0]
    By = vertices[v][1]
    
    Cx = vertices[w][0]
    Cy = vertices[w][1]
    
    if EPSILON > (((Bx-Ax)*(Cy-Ay)) - ((By-Ay)*(Cx-Ax))):  return False
    
    for p in range(0,n):
        if p == u or p == v or p == w: continue
        Px = vertices[p][0];
        Py = vertices[p][1];        
        if insideTriangle((Px,Py),((Ax,Ay),(Bx,By),(Cx,Cy))): return False;
    
    return True;
    
    
# decomposes a polygon into its triangles
def decomposePoly(vertices):
    vertices = list(vertices)
    n = len(vertices)
    result = []
    if(n < 3): return [] # not a poly!
    
    # force a counter-clockwise polygon
    if 0 >= polyArea(vertices):
        vertices.reverse()
    
    # remove nv-2 vertices, creating 1 triangle every time        
    nv = n
    count = 2*nv # error detection
    m=0
    v=nv-1
    while nv>2:
        count -= 1
        if 0>= count:
            return [] # Error -- probably bad polygon
        
        # three consecutive vertices
        u = v 
        if nv<=u: u = 0      # previous
        v = u+1
        if nv<=v: v = 0    # new v
        w = v+1
        if nv<=w: w = 0    # next

        if(polySnip(vertices,u,v,w,nv)):
            
            # record this triangle
            result.append((vertices[u],vertices[v],vertices[w]))
            
            m+=1
            # remove v from remaining polygon
            vertices.pop(v)
            nv -= 1
            # reset error detection
            count = 2*nv
    return result