Lec 2 - Perspective & Polygonal Geometry Flashcards
How do you map from a 3D space to a 2D image?
The X, Y, Z points in the 3D world (a.k.a voxels) are mapped to x, y points in the 2D world by mapping rays of light moving to/ from the observer.
What are vanishing points?
In 3D, parallel lines meet only at infinity, so the vanishing point can be thought of as the projection of a point at infinity.
What is the axis vanishing point?
If the set of lines is parallel to one of the three principal axes, the vanishing point is called an axis vanishing point.
What are some issues with spherical projection?
- Doesn’t exactly match perspective projection
2. Only a problem for very wide fields of view
What is perspective projection?
The right projection for putting a 3D scene on a flat surface. It is an abstraction of the pin-hole camera.
What is parallel projection?
Parallel projection (also known as orthographic projection) is given by: x = X y = Y That is, just drop Z coordinate!
What is a polygon?
any plane figure bounded by straight
line segments
What are the different types of polygons?
- polygonal arcs (polylines)
- polygonal boundaries (closed polylines)
- filled polygons
What are polygons used for?
as building blocks for approximating arbitrary curved arcs and regions
How are polygons represented?
- as a set of line segments
- an ordered sequence of vertices using absolute or relative coordinates
Note : Walking order convention often applies
What are some types of polygons?
Convex Concave Non-Simple Multiple boundary Star
What are convex polygons?
no internal angle is greater than 180
degrees
What are concave polygons?
there are internal angles that can be
greater than 180 degrees
How do you represent concave polygons?
as a conjunction of convex polygons (convex polygons have certain properties
that simplify geometric operations and tesselations
How can you achieve higher performance using polygons?
Level-of-detail achieves higher performance, by adapting the number of polygons used.
What is parallel projection also known as?
orthogonal projection
What is virtual camera geometry?
The image projection surface is imagined to be in front of projection center.
Geometrically equivalent to perspective projection
Often more convenient to think about this projection
What are the formulas for perspective projection?
Point P = (X,Y,Z) in 3D space has projection (x,y) in the image where
x/f = X/Z
y/f = Y/Z
f being the “focal distance” (sometimes f is called d).
In which situations do the perspective formulas apply?
These formulas apply only for camera-centred coordinates, for which perspective projection has a particularly simple form.
For arbitrarily centred coordinate systems 3D transformations are necessary
What are “one-point”, “two-point”, and “three-point”perspectives?
just special cases of perspective
projection, depending on how image plane lines up with significant planes in scene.
What is spherical projection?
The projection used by the human eye. Lens is curved, though the centre of projection isn’t at centre of the lens (therefore not planar geometric projection
What is the vertex split method?
Use an algorithm to decrease the number of polygons in a mesh by combining smaller polygons to form larger ones. This reduces the level of detail.
