3-D Transformation: In very general terms a 3D model is a mathematical representation of a physical entity that occupies space. In more practical terms, a 3D model is made of a description of its shape and a description of its color appearance.3-D Transformation is the process of manipulating the view of a three-D object with respect to its original position by modifying its physical attributes through various methods of transformation like Translation, Scaling, Rotation, Shear, etc.
Properties of 3-D Transformation:
- Lines are preserved,
- Parallelism is preserved,
- Proportional distances are preserved.
One main categorization of a 3D object’s representation can be done by considering whether the surface or the volume of the object is represented:
Boundary-based: the surface of the 3D object is represented. This representation is also called b-rep. Polygon meshes, implicit surfaces, and parametric surfaces, which we will describe in the following, are common representations of this type.
Volume-based: the volume of the 3D object is represented. Voxels and Constructive Solid Geometry (CSG) Are commonly used to represent volumetric data.
Types of Transformations:
- Translation
- Scaling
- Rotation
- Shear
- Reflection
Translation: It is the process of changing the relative location of a 3-D object with respect to the original position by changing its coordinates. Translation transformation matrix in the 3-D image is shown as –
Problem: Perform translation transformation on the following figure where the given translation distances are Dx = 2, Dy = 4, Dz = 6.
Solution: On applying Translation Transformation we get corresponding points –
