Exam Questions Flashcards
How does aliasing occur in computer graphics and what can be done to reduce its effects?
Aliasing occurs when a signal contains frequencies higher than half the sampling frequency (Nyquist frequency), in which components with higher frequencies appear (are aliased) as lower frequencies. Effects can be reduced by low-pass filtering to remove high frequencies.
A Bezier curve has five control points p1, p2, p3, p4, p5. Explain:
(i) what condition(s) must be met if these five points are to make a closed
curve?
(ii) what condition(s) must be met if the curve is to be closed and C1-
continuous at point p1?
(iii) what condition(s) must be met if we are to join two of the above Bezier
curves smoothly?
(i) p1 = p5
(ii) p1 = p5 and p2 and p4 must be colinear
(iii) Smoothness maintained by keeping the end pairs of control points
co-linear
How can a curve be a Bezier curve?
The curve must lie in the convex hull of the control points
Briefly explain the homogeneous coordinates and their role in modelling the
transformations.
Homogenous coordinates consist of adding in one coordinate to a vector space in order to write affine transformations as matrix multiplications. (ie another dimension)
Please explain how symbols L, E, D and S are used to characterise the capabilities
of rendering methods. For the following methods, please use the symbols to
characterise each method. Also, after rendering the scene, what would be present
(seen) for all the following approaches?
(a) Phong shading
(b) Ray tracing
(c) Radiosity method
Symbols are used as a regular expression L(D|S)E to describe paths where L is the light source, E is the eye, S is specular reflection and D is diffusion reflection. They characterise the paths rendered by an algorithm.
a) Phong shading = L(D|S)E (single diffuse or specular reflections). Ball will be visible, mirror will show reflection of light but not ball.
b) Ray tracing = LDSE (single diffuse but multiple specular reflections). Ball visible and mirror shows both.
c) Radiosity = LD*E (multiple diffuse) where ball is visible, mirror appears black, and bleeding of colour from ball to table (LDDE).
What’s the difference between diffuse and specular reflection?
Diffuse = normal lines not parallel, specular = normal lines of reflection are parallel
In the rendering equation [Kajiya 1986], I(x, x0) is the intensity of light passing from x’ to x:
I(x, x’) = g(x, x’)[ε(x, x’) + INTEGRAL(ρ(x, x’, x’‘)I(x’, x’’) dx’’]
Explain what is meant by g(x, x’), ρ(x, x’, x’’) and ε(x, x’), what the equation says
and why solving this equation is impractical.
ε(x, x’) = the amount of light emitted from the surface of x’ to x
g(x, x’) = visibility and attenuation term
ρ(x, x’, x’’) = scattering term for the light following the path from x’’ arriving at x’ and reflected towards x
Equation says the illumination at x from surface x’ is the sum of:
- light emitted by x’
- sum of light scattered from x’ to x from other surfaces x’’
This equation is difficult to solve because the integral is too complex to be evaluated analytically and is recursive in that the expression for I(x, x’) incorporates I(x’, x’’)
In computer graphics, name the technique that can be used to remove the
high spatial frequencies.
Anti-aliasing
What problem related to pixels and texels does MIP mapping solve?
Pixels and texels being different sizes. This always happens with perspective projections since the projected texel’s size will depend on how far away it is.
Considering Gouraud and Phong shading, which is the more realistic, especially for highly curved surfaces and why?
Phong, as only it can generate a highlight in the middle of a polygon when the illumination equation has a specular reflection term.
Assume that we have a triangle with three vertices, V0 = (−1, 1, 1), V1 = (−1, −1, 1) and V2 = (1, −1, 1). Explain whether this triangle can be backface culled or not in OpenGL and why.
The surface normal points in direction: N = (0, 0, 4) calculated via (V 1 − V 0) × (V 2 − V 0).
N · C = (0, 0, 4) · (0 0, -1) = -4 < 0
thus the triangle cannot be backface culled. In OpenGL, the camera looks along the negative z axis (C is viewing direction), and in this case, the triangle normal points directly towards the camera.
How does the z buffer algorithm handle occlusions?
By recording the depth of each rendered pixel and overwriting it if a newer, closer surface is rendered on the same location.
What’s better for rendering translucency, painters or z buffer and why?
Painters as z buffer cannot deal with translucency easily as it requires to store multiple depths in the depth buffer. While painters can render the yellow bar by blending the pixel’s colour with the previous colour using the appropriate alpha instead of overwriting it.
How does drawing a triangle strip work?
Provide 3 vertices for the first triangle draw. Next will only need 1 and will draw using last two vertices in the list.
How does drawing a triangle fan work?
Provide 3 vertices for the first triangle draw. Next will only need 1 and will draw using the first vertex and last vertex in the list.
