Week 3 - Projective Geometry, Warping and Morphing

Question 1

What do projections do?

Answer 1

Transform 3D coordinates to 2D.

Question 2

What does PP stand for?

Answer 2

Projection Plane

Question 3

What does COP stand for?

Answer 3

Centre Of Projection

Question 4

What are the 2 basic types of projections?

Answer 4

Perspective - distance from COP to PP finite.

Parallel - distance from COP to PP infinite.

Question 5

What is the main difference between parallel and perspective projection?

Answer 5

Parallel - the rays (projection lines) are parallel to eachother.

Perspective - the lines converge at the centre of projection, resulting in many visual effects, e.g. objects that are far away appear smaller, closer objects appear bigger.

Question 6

What is the view space?

Answer 6

Camera coordinate system with the camera looking down the z axis, x to the right, y up.

Question 7

What is the canonical view space?

Answer 7

Camera coordinate system with the camera looking down the z axis, x to the right, y up, and everything to be drawn within the cube [−1, 1] × [−1, 1] × [−1, 1] using parallel projection.

Question 8

What does DOP stand for?

Answer 8

Direction Of Projection

Question 9

What is orthographic projection?

Answer 9

Parallel projection where DOP (direction of projection) is perpendicular to PP (projection plane).

Question 10

What does NDC stand for?

Answer 10

Normalised Device Coordinates.

Question 11

What is the focal length f?

Answer 11

The distance between the aperture and the light-sensitive surface in the pinhole camera method.

Question 12

What is the homogeneous 3 x 4 matrix for the pinhole camera method projection?

Answer 12

f 0 0 0
0 f 0 0
0 0 1 0
Where f is the focal length.

Question 13

How is a frustrum defined?

Answer 13

A near clipping distance n, a far clipping distance f and the left l, right r, top t and bottom b clipping planes.

Question 14

In what order do coordinates get transformed?

Answer 14

Local coordinates -> world-space coordinates -> view-space coordinates -> clip coordinates -> screen coordinates

Question 15

What is viewport transform?

Answer 15

The process of transforming clip coordinates to screen coordinates.

Question 16

What is morphing (metamorphosing)?

Answer 16

An animation technique in which one graphical object is gradually turned into another.

Question 17

What is the aim of morphing?

Answer 17

To find the image of the average object between two objects.

Question 18

What is cross-dissolving?

Answer 18

The simplest method of transforming one image into another - the colour of each pixel is interpolated over time from the first image value to the corresponding second image value. AKA morphing by linear interpolation.

Question 19

Define warping.

Answer 19

The geometric transformation of graphical objects (images, surfaces or volumes) from one coordinate system to another coordinate system.

Question 20

What is image filtering?

Answer 20

Changing the range of an image.

Question 21

What is image warping?

Answer 21

Changing the domain of an image.

Question 22

Give 6 examples of parametric warps.

Answer 22

Translation, rotation, aspect, affine, perspective, cylindrical.

Question 23

How are warping and morphing related?

Answer 23

An image needs to be warped to be the correct shape for a morph (warp before cross-dissolve).

Question 24

What is forward warping?

Answer 24

Send each pixel f(x,y) to its corresponding location (x’,y’)=T(x,y) in the second image. If a pixel lands between two pixels, add contribution to several pixels, normalise later (splatting).

Question 25

What is inverse warping?

Answer 25

Get each pixel g(x’,y’) from its corresponding location (x,y)=T^-1(x’,y’) in f(x,y). Requires taking the inverse of the transform. If a pixel comes between two pixels, re-sample colour value from interpolated (pre-filtered) source image.