# Computer Graphics – 3D Translation Transformation

Last Updated : 24 Jun, 2022

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 objectâ€™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:

1. Translation
2. Scaling
3. Rotation
4. Shear
5. 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 – Where Dx, Dy, Dz are the Translation distances, let a point in 3D space is P(x, y, z) over which we want to apply Translation Transformation operation and we are given with translation distance [Dx, Dy, Dz] So, new position of the point after applying translation operation would be –

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 –

Fig.1

After performing translation transformation over the Fig.1, it will look like as below –

Fig.2

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