Scaling and shearing
- 2. Transformation Basic Transformation Additional Transformation Translation Rotation Scaling Shearing Reflection NON- RIGID BODY TRANFORMATIONS
- 3. Scaling • To change the size of an object, scaling transformation is used. • In the scaling process, we can either expand or compress the dimensions of the object. • Scaling can be achieved by multiplying the original coordinates of the object with the scaling factor to get the desired result.
- 4. Scaling Homogenous Co-ordinates Differential Co- ordinates Shape Does not Changes Size changes Sx=Sy Shape Does Changes Size changes Sx !=Sy
- 5. • Example- Original coordinates are (X, Y), Scaling factors are (SX, SY), New coordinates are (X’, Y’) ->General Representation -> Matrix Representation X' = X . SX and Y' = Y . SY (X′Y′) = (XY) Sx 0 0 Sy Scaling with respect to Origin
- 6. Scaling with respect to Origin Normal Object Object After Scaling Scaling Factor < 1 Compress(shrink) Scaling Factor > 1 Expand (stretch) Scaling Factor = 1 No Change Scaling Factor < 0 Reflect the shape
- 7. Scaling with respect to Point • STEPS- – STEP1 -> Translate to origin. – STEP2-> Scaling is done. – STEP3 -> Translate it back to that point.
- 8. Shearing • Shearing is also known as Skewing. • It is a transformation that slants the shape of an object. Shearing Transformation X- Shearing Y- Shearing X-Y -- Shearing
- 9. X- Shearing • X-Shear preserves the Y coordinate and changes are made to X coordinates. • X Sh = 1 0 Shx 1 X’= X+ (Shx * Y) Y’=Y
- 10. Y- Shearing • Y-Shear preserves the X coordinate and changes are made to Y coordinates. • Y Sh = 1 ShY 0 1 Y’=Y+ (ShY * X) X’=X
- 11. X-Y - Shearing • Here, both co – ordinates changes. • XY Sh = 1 Shy Shx 1 Y’=Y+ (ShY * X) X’=X+ (ShX * Y)