Visual computing part 2

What is a solid model?

A model using implicit functions

What is a surface model?

A model using parametric functions

What is a voxel model?

Voxel models take 3d space and say whether each pixel has matter in it or not.

What are the advantages of solid modelling?

They allow you to combine shapes

What does a 1d/2d surface model mean?

1d takes 1 input, 2d takes 2.

How do you use scan conversion to render a surface model?

Take a set of parametric equations, and break the surface down into a set of pixels, then test at each pixel

What are particle models?

Particle models have each particle associated with a set of values and repeat the shape at each particle

What do we store in the face vertex data structure?

A list of faces (with face and then their vertices) and a vertex list (with vertex, x,y,z co-ordinates and their faces)

What does face-edge-vertex data structure store?

Each stores the two other for a complete representation.

What are the stages of the graphic pipeline?

• Vertex processing

• Clipping & rasterisation

• Fragment processing

• Frame buffer processing

What happens in vertex processing?

• Convert from object to world co-ordinates, then camera space and finally clip space.

• We workout vertex normals, for lighting

What happens in clipping?

Get rid of anything that is not in the view of the eye. We create a frustum of what we can see to do this, and then do clipping for each plane of the frustum (6 times)

What is point-plane clipping?

We do the dot product with the plane normal and the point vector, if it is positive it is outside.

What happens in rasterisation?

We turn primitives into pixels, for each pixel we work out whether it is a triangle or not, this is called scan conversion

What happens in fragment processing?

This is where we compute the final fragment colours and shading, based on the texture mapping and lighting computations

What happens in frame buffer processing?

For every pixel we work out which fragment, or combination of fragments to use based of which is in front.

What are the painter’s and z-buffer algorithm

Painter’s algorithm, order all objects, paint from back to front overpainting when there’s a close object.

Z-buffer store the closest depth for each pixel, initially infinity then when drawing comprae new depth to this depth and paint if lower.

What is a pure diffuse reflection?

The surface scatters light equally in all directions.

What is a pure mirror reflection?

Line reflects along a line symmetrical about the surface normal

What are the three tpyes of lighting in the phon model?

1. Ambient

2. Diffuse (lambertian) lighting

3. Specular (phong) lighting

How do we work out diffuse relection?

diffuse reflectivity x light source intensity x cos angle (between light and surface normal)

How do we workout specular reflection?

specular reflectivity x light source intensity x cos angle (netween viewing ray and reflected ray ^ shininess coefficent.

What is the shininess coefficent

This describes the breadth of the angle of specular reflection, basically how much of an angle the viewing ray can be and still see the reflected ray. If this is smaller we have a broader angle and rougher objects. If this is larger we have a narrower angle and a smoother surface.

How do we workout ambient lighting?

ambient reflectivity x light source intensity

What can we replace cosine with for vector arithmetic?

Dot product of vectors, i.e theta is (l normal), phi is (reflection, viewing)^alpha

What are the different shading models, and how do they calculate light?

• Flat shading, per polygon

• Gourad shading, per vertex

• Phong shading, per pixel.

What do we call a model that uses a 4D function based on measurement to workout how much light is reflected?

Bidirectional reflectance distributions function (BRDF)

What are subsurface effects?

For translucent objects you have to work out the way light rays are absorbed, reflected inside and re-emited

What is a texture?

An image applied to a surface.

What are the two interpretations for workout out what part of the texture we want?

Forward and backward mapping (with bilinear interpolation)

What is bump mapping?

Where you perturb the surface normal to make it look bump.

What is displacement mapping?

Perturbing the surface height to physically change the shape of the object

What is environment mapping?

Surround the scene with a sphere, render the scene onto the sphere and colour the surface by reflection.

What are mipmaps?

Set of downsampled images of a texture, we choose fidelity basd on distance and move co-ordinates to get the right one.

What do we need to fit two polynomail curves together?

2 points, 2 gradients

What are hermite curves made up of?

Geometry matrix(2 points, 2 derivatives), blending matrix, parametisation

How do we create a basis function?

Combine blending matrix and pamatisation.

How do we work out the gradient in Bézier curves?

(0) = 3(p1 - 0)

(1) = 3(p3 - p2)

What is the convex hull property?

The curve will never pass outsidethe convex hull formed by the four control points.

What is de catelajus algorithm, after seting the control points?

How do we ensure continuity in bezier splines?

ensure p(1) = q(0)

How do ensure smoothness in Bézier splines?

p’(1) = q(0)

What are the three ways of representing curves/surfaces?

• Explicit, one axis in terms of another.

• Parametric, from a parameter (t) to a point on the curve

• Implicit, point on the curve when f(x) = 0

What are the problems with explict?

• Cant represent vertical lines.

• Can’t represent a curve that outputs two values at a single point (e.g a cicle)

What are the benefits of a parametric representation?

Using a parameter makes it easy to iterate over all points on the surface

Makes it easier to handle outputting multiple values at one point.

What values are inside, on and outside an implict surface?

What is the formula for an implict cone?

x^2 + y^2 - z^2

How can you specify size in an implict equation?

add a -w, which sets the size

How do we add (union) two implicit shapes?

Take the min of the two functions

How do we get the intersection of two implicit surfaces

Take the max of the functions

What is the zero set of an implicit function?

Surface exists if function = 0

What is the level set of an implicit function?

Function decays to 0 but dosen’t reach it, and includes a value we define.

What are benefits of level set?

We can add functions to combine instead of using min/max, create metaballs/blobs

What is marching squares/cubes?

A list of cases to tell you where to draw a line in a mesh based on which pixels are inside/outside of the implict surface

How do we convert an implicit surface to a mesh?

Marching cubes then interpolation to workout where the line cuts.

What are sudivision surfaces?

Surfaces that get better and better as we refine them, with continuity and a flexible level of detail.

What do we call the polygons we start/end with?

Control polygon and limit surface

What are the two ways we can do subdivision

1. Approximating where original vertices are moved

2. Interpolating where we add new vertices.

What is the difference between regular and irregular sampling?

Whether sampling interval is the same or not

What is aliasing?

Where we use a low sampling frequency for a high-frequency function, which means we can’t accurately depict it.

What is the Nyquist limit,

There needs to be two samples per weavelength, so limit is number of waves divided by two

What is the sampling theorem?

Assume band limited signal, to sample without alising we need to sample the highest frequency more than twice per period.

What is a band limited signal?

After a point (w) amplitude = 0

How can we reduce effect of aliasing on high frequency?

Low pass filter or add noise

How can we improve image sampling when downsizing?

Add a blur to reduce aliasing

What does an antialasing filter do?

Cut the signal at the Nyquist limit.

What is the implict form of a 2d line?

What do we call joining together multiple curves?

Piecwise modelling

What does C^0 continuity ensure?

0th order derivative is conitnous, so x points line up

What does c^1 continuity ensure?

1st derivate of the curves at each connection is continuous