3D Computer Graphics and Animation
B-Splines and NURBS surfaces
B-Splines are made of polynomials too, each with an ofset along an axis, so that there are always 4 curves being blended together to make a curve. Uniform B-Splines have a regurlar intervall between overlapping polynomial curves. Non Uniform ones do not Non uniform B-splines allow for the same complexity of shapes, but they can be told to pass through set points easily.
Non Uniform Rational B-Spline (NURBS)
Nurbs is the result of the ratio of 2 b-spline curves joined together and weighted.Bezier Curves
Polygon meshes loose quality the same way a .bmp does wen trying to display a curve
Curvilinear Quadrilaterals can be used in meshes where a cruved edge is required.
Ways to define a curve
- giving each point (not acturate)
- giving full equations (restrictive)
- construction curves from other simpler curve formule (this is the one)
Curves (functions) are constructed from 4 polyomials (n^0, n^1, n^2, n^3) Bezier curves are made by blending 4 different curves (functions) as we have above.
However, this cant make every shape possible, instead, we have to add multiple of these together end on end.
Bezier curves also have control points that change the shape of the curve, by weighting each function of the curve. Bezier curves always lie within the 4 control points as they make a polygon shape.
Geometric Primitives:
A range of geometric objects that are easy to define (described by few paramaters) Exammples can be cubes, spheres, prisms.Heigherarchical Models:
Contains multiple simpler shapes. Can be expressed in a tree to describe relationships between objects.This is more usefull for animation in higher level languages (eg C and Java)
Not usefull when a transparent surface intersect, causes intersects to become visible.
Overlaping surfaces do not get displayed in the rendered image, but still require processing. Not efficent.
Constructive Solid Geometry:
Objects created by boolean operators of other objects. CSG objects are solidScan Line Rendering:
Only works with polygons, (not solid objects, must be converted first)
Ray Tracing Rendering:
Works with CSG (solid objects) and polygons (shells).Tesselation:
An object or model described by voxels "3d pixels". Can be stored in a tree patern, with each level doubling the detail, untill the desired detail level is met.Usefull in data visualisation and 3d scans of objects.
World Space:
The minimum envelope that the object can fit inside (its bounding box)Diferent Projection Methods
Perspective Projection
Sensor is different size to area of space visible within the frame. Perspective distortion (fish eye effect) is reduced at longer distences from the camera, and begins to look like Orthographic ProjectionOrthographic Projection
Orthographic is much easier to compute/render than Perspective No distortion!3DS Max Keyboard Shortcuts
- W = Move along any axis or freeley
- E = Rotate along any axis or freeley
- R = Scale along any axis or uniformly
How to do boolean operations on two obects:
Firstly select on your first object. On the top menu bar, go to Create, Compound, Boolean. Then select the "Pick Boolean" tab on the right, click the "Pick Operand" Butto and select your second Object. Change the other settings to your desire.