Initial commit: IT Site Survey AI v2 with all features

2026-07-03 02:06:55 +00:00
commit b4fff79eda
1985 changed files with 437461 additions and 0 deletions
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+'''functions for 2D affine transformations'''
+__all__ = (
+    'nullTransform',
+    'translate',
+    'scale',
+    'rotate',
+    'skewX',
+    'skewY',
+    'mmult',
+    'combineTransforms',
+    'inverse',
+    'zTransformPoint',
+    'transformPoint',
+    'transformPoints',
+    'zTransformPoints',
+    )
+from math import cos, sin, tan, radians
+
+# constructors for matrices:
+def nullTransform():
+    return (1, 0, 0, 1, 0, 0)
+
+def translate(dx, dy=0):
+    return (1, 0, 0, 1, dx, dy)
+
+def scale(sx, sy=1):
+    return (sx, 0, 0, sy, 0, 0)
+
+def rotate(angle, cx=0, cy=0):
+    a = radians(angle)
+    sina = sin(a)
+    cosa = cos(a)
+    return (cosa, sina, -sina, cosa, cx, cy)
+
+def skewX(angle):
+    return (1, 0, tan(radians(angle)), 1, 0, 0)
+
+def skewY(angle):
+    return (1, tan(radians(angle)), 0, 1, 0, 0)
+
+def skew(ax, ay=0):
+    if ay:
+        return mmult(skewX(ax),skewY(ay))
+    else:
+        return skewX(ax)
+
+def mmult(A, B):
+    "A postmultiplied by B"
+    # I checked this RGB
+    # [a0 a2 a4]    [b0 b2 b4]
+    # [a1 a3 a5] *  [b1 b3 b5]
+    # [      1 ]    [      1 ]
+    #
+    return (A[0]*B[0] + A[2]*B[1],
+            A[1]*B[0] + A[3]*B[1],
+            A[0]*B[2] + A[2]*B[3],
+            A[1]*B[2] + A[3]*B[3],
+            A[0]*B[4] + A[2]*B[5] + A[4],
+            A[1]*B[4] + A[3]*B[5] + A[5])
+
+def combineTransforms(*T):
+    '''
+    given transform matrices in the order they should be applied generate
+    a combined transform.
+
+    combineTransforms(T0,T1,T2) == mmult(T2,mmult(T1,T0))
+                                == T2*T1*T0
+    so that T0 is applied first, then T1 and finally T2.
+    '''
+    nT = len(T)
+    return (
+            mmult(T[1],T[0]) if nT==2 
+            else mmult(combineTransforms(*T[2:]), mmult(T[1],T[0])) if nT>2
+            else T[0] if nT==1
+            else nullTransform()
+            )
+
+def inverse(A):
+    "For A affine 2D represented as 6vec return 6vec version of A**(-1)"
+    # I checked this RGB
+    det = float(A[0]*A[3] - A[2]*A[1])
+    R = [A[3]/det, -A[1]/det, -A[2]/det, A[0]/det]
+    return tuple(R+[-R[0]*A[4]-R[2]*A[5],-R[1]*A[4]-R[3]*A[5]])
+
+def zTransformPoint(A,v):
+    "Apply the homogenous part of atransformation a to vector v --> A*v"
+    return (A[0]*v[0]+A[2]*v[1],A[1]*v[0]+A[3]*v[1])
+
+def transformPoint(A,v):
+    "Apply transformation a to vector v --> A*v"
+    return (A[0]*v[0]+A[2]*v[1]+A[4],A[1]*v[0]+A[3]*v[1]+A[5])
+
+def transformPoints(matrix, V):
+    r = [transformPoint(matrix,v) for v in V]
+    if isinstance(V,tuple): r = tuple(r)
+    return r
+
+def zTransformPoints(matrix, V):
+    return list(map(lambda x,matrix=matrix: zTransformPoint(matrix,x), V))