#================================================================== # 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= 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