TRANSFORMATION
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This document summarizes different types of geometric transformations including translation, scaling, and rotation. It defines 2D and 3D translation as moving an object along straight lines by adding increments to coordinate values. Scaling is described as enlarging or reducing an object's size using scaling factors. Rotation is defined as moving an object along a circular path in the xy-plane or xyz coordinates without deformation. Equations for representing each transformation in matrix and homogeneous form are provided.
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Transformation
1. The document discusses different types of 2D and 3D transformations including translation, scaling, and rotation.
2. Translation moves an object along a straight line by adding increments to the x, y, and z coordinates. Scaling enlarges or reduces the size of an object by multiplying the x and y coordinates by scaling factors.
3. Rotation moves an object along a circular path in the xy plane or xyz coordinates without deforming the object. Rotations can be represented using trigonometric functions or transformation matrices.
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This document discusses 2D and 3D geometric transformations. It describes two types of transformations: geometric transformations that alter the object itself, and coordinate transformations that alter the coordinate system. Several common 2D geometric transformations are covered, including translation, rotation, scaling, reflection and shear. Matrix representations are introduced to combine multiple transformations into a single operation. The concept of homogeneous coordinates is explained for representing 2D transformations with 3x3 matrices. Finally, a general method for 2D rotation around a pivot point is described.
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1) 2D geometric transformations include translations, scaling, and rotations. They can be represented by transformation matrices.
2) Translation moves an object by adding offsets to x and y coordinates. It can be represented by a 3x3 matrix with 1s on the diagonal and offsets as the last column.
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TRANSFORMATION-CG.pptx
This document discusses various geometric transformations used in computer graphics including translation, rotation, scaling, shearing, reflection, and their mathematical representations. It also covers topics like matrix representation, homogeneous coordinates, and composite transformations. Translation moves an object along a straight path. Rotation repositions an object around a circular path by a specified angle. Scaling changes an object's size. Shearing distorts the shape of an object. Reflection produces a mirror image. Matrix representation stores transformations. Homogeneous coordinates provide a unified treatment of transformations and projections. Composite transformations combine multiple transformations into one.
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TRANSFORMATION
- 1. SENTHUR POLYTECHNIC COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING 4020530/ COMPUTER INTEGRATED MANUFRACTION SEMINAR PRESENTATION Submitted by BALAMURUGAN. A ( 22216385 ) Seminar Topic Transformation
- 3. TRANSLATION 1. Translation Translation is the simplest form of transformation. It is rigid body transformation that moves the object without any deformation. 2D translation move the object on x, y plane along straight line By adding increments in x-axis, y-axis, 3D translation move the object on xyz coordinates along straight line adding increments in x-axis, y-axis and z-axis,
- 4. The above equation can be written in matrix From as (X’, Y’) = (X, Y) + (tx, ty) or (X’/Y’) = (X/Y) + (tx/ty) The homogeneous representation of above matrix is X’ 1 0 tx X Y’ = 0 1 ty Y 1 0 0 1 1
- 5. P’ = Tt × P Tt = Transformation matrix for translation Scaling Scaling transfoation is used to enlarge or reduce The size of the object. Let (X,Y) => are the initial coordinate values of the object (X’, Y’) => final coordinate values of the object Sx => scaling factor along the x-axis Sy => scaling factor along the y-axis
- 6. Then x’ = x. Sx and Y’ = y. Sy In matrix from X’ Sx 0 X = Y’ 0 Sy Y The above equation is written in homogenous From as follows.
- 7. ROTATION Rotation is the rigid body transformation that Move the object along the circular path in xy plane or In xyz coordinate without any deformation X = r cos ∅ Y = r cos ∅ The above equation is written in homogenous form as follows X’ = cos o - sin o 0 0 X Y’ = sin o - cos o 0 0 Y Z’ = 0 0 1 0 Z 1 = 0 0 0 1 1
- 8. 😇 THANKS YOU 😇