Week 3 - Projective Geometry, Warping and Morphing Flashcards
What do projections do?
Transform 3D coordinates to 2D.
What does PP stand for?
Projection Plane
What does COP stand for?
Centre Of Projection
What are the 2 basic types of projections?
Perspective - distance from COP to PP finite.
Parallel - distance from COP to PP infinite.
What is the main difference between parallel and perspective projection?
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.
What is the view space?
Camera coordinate system with the camera looking down the z axis, x to the right, y up.
What is the canonical view space?
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.
What does DOP stand for?
Direction Of Projection
What is orthographic projection?
Parallel projection where DOP (direction of projection) is perpendicular to PP (projection plane).
What does NDC stand for?
Normalised Device Coordinates.
What is the focal length f?
The distance between the aperture and the light-sensitive surface in the pinhole camera method.
What is the homogeneous 3 x 4 matrix for the pinhole camera method projection?
f 0 0 0
0 f 0 0
0 0 1 0
Where f is the focal length.
How is a frustrum defined?
A near clipping distance n, a far clipping distance f and the left l, right r, top t and bottom b clipping planes.
In what order do coordinates get transformed?
Local coordinates -> world-space coordinates -> view-space coordinates -> clip coordinates -> screen coordinates
What is viewport transform?
The process of transforming clip coordinates to screen coordinates.
What is morphing (metamorphosing)?
An animation technique in which one graphical object is gradually turned into another.
What is the aim of morphing?
To find the image of the average object between two objects.
What is cross-dissolving?
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.
Define warping.
The geometric transformation of graphical objects (images, surfaces or volumes) from one coordinate system to another coordinate system.
What is image filtering?
Changing the range of an image.
What is image warping?
Changing the domain of an image.
Give 6 examples of parametric warps.
Translation, rotation, aspect, affine, perspective, cylindrical.
How are warping and morphing related?
An image needs to be warped to be the correct shape for a morph (warp before cross-dissolve).
What is forward warping?
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).
What is inverse warping?
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.
