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TRANSFORMATION-CG.pptx

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TRANSFORMATION-CG.pptx

  1. 1. Computer Graphics By Ms.N.RUBA Asst. Prof / CA BSCW, Thanjavur.
  2. 2. BASIC TRANSFORMATION Transactions are helpful in changing the position,size,orientation,shape,etc.,of the object. There are three basic rigid transformation. *Translation *Rotation *Scaling The derived geometrical transformation is: *Reflection *Shearing
  3. 3. The translation is repositioning an object along a straight-line path from one coordinate location to another coordinate location. The translation is the rigid body transformation that saves an object without deformation. A translation moves to a different position on the screen. X’=X + tx Y’=Y + ty TRANSLATION P=[X]/[Y] P’=[X’][Y’] we can also write as: P’=P+T T=[tx]/[ty]
  4. 4. ROTATION It is the transformation that is used to reposition one object along the circular path in the XY plane. We specify a rotation angle TITA and the portion of the rotation point A and B about which the object is being rotated to generate a rotation. P’=P.R Where R is the rotation matrix
  5. 5. SCALING Scaling is the transformation that is used to change the object’s size. The Operation is carried out by multiplying the coordinate value(X,Y)with Sx and Sy scaling factors. X’=X. Sx and Y’=Y. Sy P’=P . S
  6. 6. SHEARING Shearing is the transformation used to change the shape of an existing object in the 2D plane. The size of the object changes along the x direction as well as the Y direction. Reflection Reflection is the mirror image of the original object. In other words, we will say that it is the rotation operation with 180 degree. In reflection transformation, the object’s size does not change.
  7. 7. MATRIX REPRESENTATION Matrix representation is a method used by a computer language to store matrices of more than one dimension in memory. Fortran and C use different schemes for their native arrays. Fortran uses “Column Major”, in which all the elements for a given column are stored contiguously in memory. P’=M1 +P +M2 x=xh/h+ y=yh/h
  8. 8. HOMOGENEOUS COORDINATE Homogeneous coordinates have a natural application to computer graphics ; they form a basis for the projective geometry used extensively to project a three dimensional scene onto a two dimensional image plane. They also unify the treatment of common graphical transformation and operations. P’= T(t1…….tp) P’=S(t1……….tp) P
  9. 9. HOMOGENEOUS COORDINATE EXAMPLES
  10. 10. COMPOSITE TRANSFORMATION A number of transformation or sequence of transformation can be combined into single one called as composition. The process of combining is called as concatenation. Suppose we want to perform rotation about an arbitrary point, then we can perform it by the sequence of three transformation. 1. Translation 2. Rotation 3. Reverse Translation
  11. 11. EXAMPLE SHOWING COMPOSITE TRANSFORMATION
  12. 12. THANK YOU

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