Computer Graphics20815 marksNumerical: Rotation and translation transformationHomogeneous Coordinate and 2D Composite Transformations
Given a triangle with vertices A(2,3), B(5,5), C(4,3) by rotating 90 degrees about the origin and then translating two units in each direction. Use the homogeneous transformation matrix to find the new vertices of the triangle.
Given a triangle with vertices A(2,3), B(5,5), C(4,3) by rotating 90 degrees about the origin and then translating two units in each direction. Use the homogeneous transformation matrix to find the new vertices of the triangle. [5]
- Vertices: $A(2,3)$, $B(5,5)$, $C(4,3)$ - Rotation: $\theta = 90°$ about origin (counterclockwise, standard convention) - Translation: $tx = 2$, $ty = 2$ $$R(90°) = \begin{bmatrix} \cos90° & -\sin90° & 0 \ \sin90° & \cos90° & 0 \ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 0 & -1 & 0 \ 1 & 0 & ...