BIT304 · TU past paper
Computer Graphics 2080 question paper
The complete TU 2080 exam paper for Computer Graphics (BIT304), all 12 questions with solved model answers written to the mark scheme.
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- 110 marksSutherland-Hodgman polygon clipping algoriHideAnswer
How Can Polygons Be Clipped? Describe Gouraud Shading Model with Necessary Derivations [10]
Definition: Polygon clipping is the process of removing portions of a polygon that lie outside a specified clipping window while retaining and correctly connecting the portions inside. The most common polygon clipping method processes th...
- 210 marksNumericalBresenham's line drawing algorithmHideAnswer
Write the algorithm for Bresenham's line drawing? Digitize a line with end points A(6, 9) and B(10,5) using Bresenham's line drawing algorithm.[10]
- Endpoint A: $(x1, y1) = (6, 9)$ - Endpoint B: $(x2, y2) = (10, 5)$ 1. Input the two endpoints $(x1, y1)$ and $(x2, y2)$. 2. Compute $\Delta x = x2 - x1$ and $\Delta y = y2 - y1$. 3. Plot the first point $(x1, y1)$. 4. Calculate the ini...
- 310 marksNumericalParallel projectionHideAnswer
Differentiate between parallel and perspective projection. Perform the rotation of triangle with vertices A(5,7), B(12,85) and C(5,3) counterclockwise 30 degree about the pivot point (5,3).[10]
Model Answer: Parallel vs Perspective Projection and Triangle Rotation
Part 1: Parallel vs Perspective Projection
Aspect Parallel Projection Perspective Projection Projectors Projection lines (projectors) are parallel to each other Projectors converge to a single point (center of projection) Center of projection At infinity At a finite distance Vanishing point None; parallel lines remain parallel One or more vanishing points; parallel lines converge Depth realism Does not depict realistic depth; size independent of distance Realistic depth; distant objects appear smaller (foreshortening) Scale/proportion True dimensions and proportions preserved Scale varies with distance from viewpoint Mathematics Simpler (orthographic/oblique matrices, no division) More complex; requires division by the depth coordinate Applications Engineering/technical drawings, CAD, blueprints Realistic rendering, architecture, games, photography
Part 2: Rotation of Triangle 30° CCW about Pivot (5,3)
Given data:
- Vertices: $A(5,7)$, $B(12,85)$, $C(5,3)$
- Angle: $\theta = 30^\circ$ counterclockwise
- Pivot: $P(p_x,p_y) = (5,3)$
Rotation about a pivot: $$x' = p_x + (x-p_x)\cos\theta - (y-p_y)\sin\theta$$ $$y' = p_y + (x-p_x)\sin\theta + (y-p_y)\cos\theta$$
Trig values: $\cos 30^\circ = 0.8660$, $\sin 30^\circ = 0.5$
Vertex A(5,7): $\Delta x = 0,\ \Delta y = 4$ $$x'_A = 5 + (0)(0.866) - (4)(0.5) = 5 - 2 = 3$$ $$y'_A = 3 + (0)(0.5) + (4)(0.866) = 3 + 3.464 = 6.464$$ $$A' = (3,\ 6.464)$$
Vertex B(12,85): $\Delta x = 7,\ \Delta y = 82$ $$x'_B = 5 + (7)(0.866) - (82)(0.5) = 5 + 6.062 - 41 = -29.938$$ $$y'_B = 3 + (7)(0.5) + (82)(0.866) = 3 + 3.5 + 71.012 = 77.512$$ $$B' = (-29.938,\ 77.512)$$
Vertex C(5,3): $\Delta x = 0,\ \Delta y = 0$ (this is the pivot) $$x'_C = 5 + 0 - 0 = 5,\quad y'_C = 3 + 0 + 0 = 3$$ $$C' = (5,\ 3)$$
Final Result:
- $A' \approx (3.00,\ 6.46)$
- $B' \approx (-29.94,\ 77.51)$
- $C' = (5,\ 3)$
(Note: vertex B(12,85) appears unusually large for a triangle, but the computation follows the given data exactly.)
- 45 marksMotion capture and keyframe animationHideAnswer
Explain motion capture with an example. [5]
Motion capture (often abbreviated as mocap) is a technology used to record and digitize the movement of real actors or objects in three-dimensional space. The captured motion data is then transferred to digital characters or models in co...
- 55 marksBezier curves and propertiesHideAnswer
Explain about parametric curve. Describe the properties of Bezier curve. [5]
A parametric curve is a curve defined by parametric equations where the coordinates (x, y) are expressed as functions of a parameter t: - x = f(t) - y = g(t) where t ranges over an interval [a, b]. Instead of expressing y explicitly as a...
- 65 marksWireframe representation of 3D objectsHideAnswer
Explain the wireframe representation of 3D objects. [5]
Wireframe representation is a method of displaying 3D objects using only edges and vertices, without rendering surfaces or faces. The object appears as a skeleton made of lines connecting corner points in 3D space. 1. Structure - Consist...
- 75 marksPolygon creation in OpenGLHideAnswer
How does a polygon can be created in OpenGL? Illustrate with an example. [5]
In OpenGL, polygons are created by specifying a sequence of vertices and enclosing them within a pair of functions that define the primitive type. The basic approach involves: 1. Begin a primitive using glBegin() 2. Specify vertices usin...
- 85 marksZ-buffer method and limitationsHideAnswer
Write short notes a. Z-Buffer b. Polygon Table [5]
Definition: Z-Buffer (also called Depth Buffer) is a hidden surface removal technique that stores the depth (z-coordinate) value of each pixel on the screen. Working Principle: - Maintains a 2D array of depth values corresponding to each...
- 95 marksRandom scan display systemsHideAnswer
Explain architecture of random scan display systems with suitable diagram. [5]
A random scan display (also called vector display or stroke-writing display) is a display system that draws images by directing an electron beam to specific points on the screen in any arbitrary order, rather than scanning the entire scr...
- 105 marksCohen-Sutherland line clipping algorithmHideAnswer
Explain Cohen-Sutherland Line Clipping algorithm with example. [5]
The Cohen-Sutherland algorithm is a line clipping algorithm used to determine which portions of a line lie within a rectangular clipping window and should be displayed. It uses a region coding scheme to efficiently identify and clip line...
- 115 marksNumericalShearing transformationHideAnswer
Reflect a line segment having end points (9,3) and (12,10) about a line X = 7. Draw initial and final result graph as well. [5]
- Endpoint A = $(9, 3)$ - Endpoint B = $(12, 10)$ - Line of reflection: $x = 7$ (vertical line, $k = 7$) For any point $(x, y)$ reflected about the vertical line $x = k$: $$(x, y) \rightarrow (2k - x,\ y)$$ The $y$-coordinate is unchange...
- 125 marksAmbient light and ambient reflectionHideAnswer
Explain ambient light, diffuse reflection and specular reflection with examples. [5]
Definition: Ambient light is the general, non-directional illumination present in a scene that comes from all directions uniformly. It represents light that has been scattered and reflected so many times in an environment that its origin...