Transcription of COORDINATE TRANSFORMATIONS
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COORDINATE TRANSFORMATIONS
PLATE 17-1 COORDINATE TRANSFORMATIONSTWO DIMENSIONAL TRANSFORMATIONSThe two dimensional conformal COORDINATE transformation isalso known as the four parameter similarity transformationsince it maintains scale relationships between the two Scaling2. Rotation3. Translation in X and YxYXy1342 BCA1324 ABC(a)(b)PLATE 17-22D CONFORMAL TRANSFORMATIONSS teps in transforming coordinates measured in thecoordinate system shown in (b) into that shown in (a).SABaABbxSxySyPLATE 17-32D CONFORMAL TRANSFORMATIONSStep 1: SCALING. To make the length between A and Bin (b) equal to the length between A and B in (a).andCall this scaled system (b ).TyY'XX'Yx'Y'4Y44X'4X4 Txy PLATE 17-42D CONFORMAL TRANSFORMATIONSStep 2: ROTATION. Rotate COORDINATE system in scaledsystem (b ) so that points in (b ) coincide with pointsin (X , Y ) ' = x' Cos - y' Sin Y' = x' Sin + y' Cos PLATE 17-52D CONFORMAL TRANSFORMATIONSSTEP 3: TRANSLATIONSUse coordinates of common point in scaled-rotated system(X , Y ) to compute T and = X - X xT = Y - Y yTan1baSaCosPLATE 17-6 OBSERVATION EQUATIONSC ombining equations for scale, rotation, and translationyields:X = (S Cos )x - (S Sin )y + TXY = (S Sin )x + (S Cos )y + TYLet S Cos = a, S Sin = b, T = c, and T = dXYAdd residuals to develop observation - by + c = X + vXay + bx + d = Y + vYNOTE:Axaya10yaxa01xbyb10ybxb01xcyc10yc xc01
COORDINATE TRANSFORMATIONS TWO DIMENSIONAL TRANSFORMATIONS The two dimensional conformal coordinate transformation is ... data using a 2D projective transformation. Pt X Y x y x y 1 1420.407 895.362 90.0 90.0 0.3 0.3 2 895.887 351.398 50.0 40.0 0.3 0.3 3 -944.926 641.434 -30.0 20.0 0.3 0.3
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