Sampling: Antialiasing - Intro

Transcription

1 Sampling: Antialiasing - Intro Aliasing effects occur due to fact that the basic tracer 1. Casts a single ray per pixel 2. Casts the rays in a regular pattern Only a single color is possible for a given pixel No consideration of adjacent pixels is given General problems that result are 1. Staircasing (jaggies) and loss of detail 2. Loss of fine detail Note: Detail smaller than 1 pixel cannot be captured 1

2 3. Moire patterns Sampling: Antialiasing - Intro (2) Left image maps f(x, y) = 1 2 (1 + sin(x2 y 2 )) with relatively little aliasing effects Right image is at greater resolution; note emergence of Moire patterns 2

3 Sampling: Antialiasing - Solutions Remedies include 1. Increasing resolution This does not solve the problem It only reduces the effects 3

4 2. Regular sampling Sampling: Antialiasing - Solutions (2) This involves dividing each pixel into subpixels Rays are cast from the subpixels Results are averaged If a pixel is subdivided into an n n grid, there will be n 2 samples per pixel Examples: left: One sample per pixel center: 16 samples per pixel right: Magnified image 4

5 Sampling: Antialiasing - Solutions (3) This still produces artifacts as it uses a regular sampling pattern 5

6 3. Random sampling Sampling: Random Sampling This approaches randomly selects subpixels to cast rays from Not restricted to an n n grid Such a random distribution is referred to as noise Problems: Samples can cluster, leaving large unsampled areas 6

7 Sampling: Characteristics of Good Sampling A good sampling technique should 1. Distribute points evenly over the unit square This minimizes clumps and gaps 2. Distribute points evenly for projections onto both the X and Y axes If uneven, some parts of scene will be under or over sampled 3. Guarantee that points are no closer than some minimum distance A pattern that meets are 3 criteria is called well-distributed If enough samples are used, most techniques provide similar results The question is: How many is enough to produce satisfactory results? Satisfactory means that the amount of aliasing and noise are acceptable Poor techniques can require 3 the number of samples required by a good technique This is a big issue since rendering is expensive Random sampling meets none of the three criteria 7

8 Sampling: Techniques 1. Jittering Combines aspects of regular pattern with randomness Pixel subdivide into an n n grid Rays cast from a random point from within each subpixel This insures an even distribution, but with randomness incorporated Samples are stratified A domain is stratified by dividing it into regions that do not overlap and completely cover the domain Each region is called a stratum Jittering samples each stratum This is better than random sampling in which all samples could come from the same stratum 8

9 Sampling: Techniques(2) Generates better image than either of the above approaches left: 1 sample per pixel right: 64 jittered samples per pixel 2. N-Rooks Sampling Given an n n grid, generate samples along the diagonal Called n-rooks technique because if rooks (castles) were placed on the diagonal of a chess board, they could not capture each other Provides a good 1D distribution To achieve a good 2D distribution, randomly shuffle the x, y coordinates while keeping the n-rooks condition Resulting 2D distribution not guaranteed to be good In general, no better than random distribution 9

10 Sampling: Techniques(3) 3. Multi-jittered Sampling Combines jittering with the n-rook approach Uses a grid and a subgrid In general, for n = x 2 (a) Grid is x x (b) Subgrid is x 2 x 2 In the grid, generate one sample per cell of the subgrid Samples must meet the n-rooks condition This will generate 16 samples in a 4 4 grid Shuffle the x, y coordinates while maintaining the n-rook condition Insures a good 1D distribution and a better 2D distribution than the random, jittered, or n-rooks techniques 10

11 Sampling: Techniques(4) 4. Hammersley Sampling This approach based on numeric representation of binary numbers Let binary representation of where a j (i) = 0, 1 i = n a j (i)2 j = a a j=0 Hammersley sequence is based on radical inverse of i: Φ 2 (i) [0, 1] = n a j (i)2 j 1 = a a j=0 This function generates a value by reflecting the binary representation of a number across the decimal point and converting the result back to base 10 For example, = 1/2 + 1/8 + 1/16 = 11/16 = Note: The function does not have to be restricted to base 2 in the general case The Hammersley sequence of n 2D samples p j is p j = (x i, y i ) = [ i n, Φ 2(i)] This is projected onto the unit square The resulting sequence is (a) Fixed for a given n (b) Not random (c) Evenly distributed in the 1D projection (d) Evenly distributed in 2D (e) Maintains a minimum distance between samples 11

12 Sampling: Techniques(5) 12

13 Sampling: Notes None of the sampling techniques is able to account for fine detail Sampling is used for more than just antialiasing: 1. Depth of field (lens sampling) 2. Area lights and soft shadows (source sampling) 3. Global illumination and specular reflection (BRDF and BTDF sampling) 13