Computer Graphics · Unit 4 · 5 hrs
Three-Dimensional Geometric Transformation
Exam-focused notes for Three-Dimensional Geometric Transformation (Computer Graphics, CSC214): what the TU syllabus asks and how it has actually been tested, with 5 solved past questions from this unit.
What this unit covers
- Three-Dimensional translation, Rotation, Scaling, Reflection and Shearing
- Three-Dimensional Composite Transformations
- Three-Dimensional Viewing: Viewing pipeline, world to screen viewing transformation, Projection concepts(Orthographic, parallel, perspective projections)
Three-Dimensional Viewing
Differentiate between parallel projection and perspective projections. [5]
Parallel Projection: In parallel projection, the distance from the center of projection (COP) to the projection plane is infinite. Parallel lines are drawn from each vertex of the object in a specified direction until they intersect the view plane. A direct...
Full solved answer →Differentiate between parallel and perspective projection with suitable diagram. Illustrate the window to viewport transformation with example.[10]
--- Parallel Projection: In parallel projection, the projectors (lines of projection) are parallel to each other and perpendicular (or at an angle) to the projection plane. The center of projection is at infinity. Perspective Projection: In perspective proj...
Full solved answer →Question
Define orthographic, parallel, and perspective projections. Consider a region defined by the position vector P below, relative to global XYZ axis system. It is rotated by +30° about X-axis and passes through points (1.5, 1.5, 1.5). Find the final position of the region.
$$P = \begin{bmatrix} 1 & 1 & 2 & 1 \ 2 & 1 & 2 & 1 \ 2 & 2 & 2 & 1 \ 1 & 2 & 2 & 1 \end{bmatrix}$$
[10]
Parallel Projection: The projectors (lines joining object points to the view plane) are parallel to each other; the centre of projection is located at infinity. It preserves relative proportions and is used for engineering/technical drawings. Orthographic P...
Full solved answer →Differentiate between orthographies, parallel, and perspective projections. [5]
Projection is the process of mapping a 3D object onto a 2D plane (view plane). The two major types are Parallel Projection and Perspective Projection. Orthographic projection is a subtype of parallel projection. --- - In parallel projection, the projectors ...
Full solved answer →Three-Dimensional translation, Rotation, Scaling, Reflection and Shearing
Derive the relation for three-dimensional translation and rotation. [5]
--- Translation moves a point linearly in space. Let point P(x, y, z) be translated by translation vector T(tx, ty, tz) to produce image point P'(x', y', z'). The translated coordinates are obtained by adding the translation distances to each coordinate: $$...
Full solved answer →Make Unit 4 stick
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