Computer Graphics Chapter 4 Attributes of Graphics Primitives Somsak Walairacht, Computer Engineering, KMITL 1
Outline OpenGL State Variables Point Attributes t Line Attributes Fill-Area Attributes Scan-Line Polygon-Fill Algorithm Fill Methods for Areas with Irregular Boundaries Character Attributes Antialiasing 01074410 / 13016218 Computer Graphics 2
Introduction A parameter that affects the way a primitive i i is to be displayed d is referred to as an Attribute Parameter For example, lines can be dotted or dashed, fat or thin, and blue or orange Areas might be filled Text can appear from left to right, slanted diagonally, or in vertical 01074410 / 13016218 Computer Graphics 3
OpenGL State Variables For example, Color and other primitive attributes, the current matrix mode, the elements of the model-view matrix, the current position for the frame buffer, and the parameters for the lighting effects in a scene Remained in effect until their new values are specified We can query the system to determine the current value of a state parameter 01074410 / 13016218 Computer Graphics 4
Point Attributes Two attributes for points: color and size Color components are set with RGB values or an index into a color table Size is an integer multiple of the pixel size 01074410 / 13016218 Computer Graphics 5
Line Attributes Three basic attributes: color, width, and style Additionally, lines may be generated with other effects, such as pen and brush strokes 01074410 / 13016218 Computer Graphics 6
Fill-Area Attributes Most graphics packages limit fill areas to polygons, because they are described with linear equations Further restriction requires fill areas to be convex 01074410 / 13016218 Computer Graphics 7
Fill-Area Attributes (2) There are two basic procedures for filling an area on raster systems 1 (simple shape) Determines the overlap intervals for scan lines that cross the area Pixel positions along these overlap intervals are set to the fill color 2 (not so simple shape) Start from a given interior position and paint outward pixel-by-pixel until boundary 01074410 / 13016218 Computer Graphics 8
Fill-Area Attributes (3) The scan-line approach is usually applied to simple shapes such as circles or regions with polyline boundaries General graphics packages use this fill method While using a starting interior point, it is useful for filling areas with more complex boundaries and in interactive painting systems 01074410 / 13016218 Computer Graphics 9
Fill Styles 01074410 / 13016218 Computer Graphics 10
Color-Blended Fill Regions A pattern could be combined with background colors Using a transparency factor that determines how much of the background should be mixed with the object color 01074410 / 13016218 Computer Graphics 11
Color-Blended Fill Regions (2) Simple logical or replace operations 01074410 / 13016218 Computer Graphics 12
Color-Blended Fill Regions (3) Algorithm using color-blending Soft-fill or Tint-fill algorithms A foreground color F with a single background color B, where F = B The current RGB color P of each pixel within the area to be refilled is some linear combination of F and B P = tf + (1 t)b where the transparency factor t has a value between 0 and 1 P = (P R, P G G, P B B), F = (F R, F G G, F B B), B = (B R, B G G, B B B) t = P k B k / F k B k where k = R, G, or B; and F k B k Similarly, a foreground color is to be merged with multiple background color P = t 0 F+t 1 B 1 +(1 t 0 t 1 )B 2 01074410 / 13016218 Computer Graphics 13
General Scan-Line Polygon-Fill Algorithm A scan-line fill of a region is performed by first determining the intersection positions of the boundaries of the fill region with the screen scan lines Then the fill colors are applied to each section of a scan line that lies within the interior of the fill region The scan-line fill algorithm identifies the same interior regions as the odd-even rule 01074410 / 13016218 Computer Graphics 14
General Scan-Line Polygon-Fill Algorithm (2) Basic scan-line procedure: 2 steps 1. Edge intersections are sorted from left to right 2. Then the pixel positions between, and including, each intersection pair are set to the specified fill color จดร วมขอบอย ด านเด ยวก น จ ดรวมขอบอย ดานเดยวกน Sort x-intersection ascending จ ดร วมขอบอย คนละด าน 01074410 / 13016218 Computer Graphics 15
General Scan-Line Polygon-Fill Algorithm (3) To split those vertices that should be counted as one intersection When the endpoint y coordinates of the two edges are increasing, the y value of the upper endpoint for the current edge is decreased by 1 When the endpoint y values are monotonically decreasing, the y coordinate of the upper endpoint of the edge following the current edge is decreased by 1 next current current next 01074410 / 13016218 Computer Graphics 16
General Scan-Line Polygon-Fill Algorithm (4) Coherence properties can be used in computer-graphics algorithms to reduce processing It often involves incremental calculations l applied along a single scan line or between successive scan lines 01074410 / 13016218 Computer Graphics 17
Determining Fill-Area Edge Intersections Two successive scan lines crossing the left edge of a triangle The slope of this edge m = (y k+1 y k )/(x k+1 x k ) The change in y coordinates y k+1 y k = 1 Each successive x intercept can thus be calculated by adding the inverse of the slope and rounding to the nearest integer x k+1 = x k +1/m 01074410 / 13016218 Computer Graphics 18
Coherence Methods (Truncate) counter = 0 counter += dx If counter dy then { x++, counter -= dy } y++ Method 1 Method 2 (Rounding) counter = 0 counter += 2dx If counter dy then { x++, counter -= 2dy } y++ m=7/3 [1] [2] 01074410 / 13016218 Computer Graphics 19
Sorted Edge Table Proceeding around the edges in either a clockwise or a counterclockwise order, sorted on the smallest y value of each edge Only nonhorizontal edges are entered into the table For a particular scan line, the maximum y value for that edge, the x-intercept value (at the lower vertex) for the edge, the inverse slope of the edge For each scan line, the edges are in sorted order from left to right 01074410 / 13016218 Computer Graphics 20
Sorted Edge Table (2) 01074410 / 13016218 Computer Graphics 21
Sorted Edge Table (3) Process the scan lines from the bottom of the polygon to its top -> active edge list for each scan line For a scan line contains all edges crossed, uses iterative coherence calculations to obtain the edge intersections For each scan line, fill interior pixel at x-intercept values from left to right 01074410 / 13016218 Computer Graphics 22
Scan-Line Fill of Convex Polygons Uses coordinate extents to determine which edges cross a scan line Intersection calculations with these edges then determine the interior pixel span Any vertex crossing is counted as a single point Some graphics packages restrict fill areas to be triangles This makes filling even easier 01074410 / 13016218 Computer Graphics 23
Scan-Line Fill for Regions with Curved Boundaries For simple curves such as circles or ellipses, apply fill methods for convex polygons Each scan line cross just two boundary intersections Determine these two intersection points using the incremental calculations in the midpoint method Simply fill in the horizontal pixel spans Applies symmetric property between quadrants 01074410 / 13016218 Computer Graphics 24
Fill Methods For Areas with Irregular Boundaries Boundary-fill algorithm, is employed in interactive painting packages, where interior points are easily selected Select a fill color, specify the boundary color, and pick an interior i point 01074410 / 13016218 Computer Graphics 25
Fill Methods For Areas with Irregular Boundaries (2) Two methods for processing neighboring pixels from a current test position 4-connected : pixel positions that are right, left, above, and below the current pixel 8-connected : Neighboring positions to be tested includes the four diagonal pixels 01074410 / 13016218 Computer Graphics 26
Boundary Fill 01074410 / 13016218 Computer Graphics 27
Flood-Fill Algorithm Paints areas by replacing a specified interior color instead of searching for a particular boundary color Starting from a specified interior point (x, y) and reassign all pixel values to a given interior color Using either a 4-connected or 8-connected approach 01074410 / 13016218 Computer Graphics 28
Character Rendering Letters, digits, non-alphanumeric Font overall design style of a set of characters Times New Roman, Courier, Arial Fonts can vary in appearance Normal, Bold, Italic Rendering techniques Bitmap font Outlined fonts - Examples are PostScript Type 1 and Type 3 fonts, TrueType and OpenType. 01074410 / 13016218 Computer Graphics 35
Character Attributes Characters with attributes such as font, size, color, and orientation Color settings for displayed text can be stored in the system attribute list Adjusts text size by scaling the overall dimensions (height h and width) of characters or by scaling only the height or the width 01074410 / 13016218 Computer Graphics 36
Character Attributes (2) The orientation for a character string can be set according to the direction of a character up vector 01074410 / 13016218 Computer Graphics 37
About Point Font size usually denoted in point (e.g. 10-point, 12- point) Denotes height of the characters in inches Atermfromtypography typography Smallest unit of measure We are concerned with desktop publishing (DTP) point, also called the PostScript point Not the original typographical point 1 DTP point = 1/72 of an inch or approx 0.0139 inch 01074410 / 13016218 Computer Graphics 38
Antialiasing Jagged or stair-step appearance happens because the sampling process digitizes coordinate points on an object to discrete integer pixel positions This distortion ti due to low-frequency sampling (undersampling) is called aliasing 01074410 / 13016218 Computer Graphics 39
Aliasing Starting with a continuous signal, then sample the signal at discreet points Those samples are then used to reconstruct a new signal It is intended to represent the original signal However, the reconstructed signals are a false representation of the original i signals In the English language, When a person uses a false name, it is known as an alias So, it was adapted in signal analysis to apply to falsely represented signals Aliasing in computer graphics usually results in visually distracting artifacts A lot of effort goes into trying to stop it This is known as antialiasing 01074410 / 13016218 Computer Graphics 40
Nyquist Frequency Theoretically, in order to adequately reconstruct a signal of frequency x, the original signal must be sampled with a frequency of greater than 2x This is known as the Nyquist Sampling Frequency or Nyquist Limit However, this is assuming that we are doing a somewhat idealized sampling and reconstruction In practice, it s probably a better idea to sample signals at a minimum of 4x 01074410 / 13016218 Computer Graphics 45
Nyquist Sampling Frequency To avoid losing information from such periodic objects, we need to set the sampling frequency to at least twice that of the highest frequency occurring in the object f s = 2 f max 01074410 / 13016218 Computer Graphics 46
Nyquist Sampling Interval The sampling interval should be no larger than one-half the cycle interval x s = x cycle / 2 where x cycle = 1/ f max 01074410 / 13016218 Computer Graphics 47
Antialiasing (2) To increase sampling rate, simply displays objects at higher h resolution Limitations: How big the frame buffer Refresh rate 60 fps or more Modify pixel intensities Appropriately varying the intensities iti of pixels along the boundaries of primitives 01074410 / 13016218 Computer Graphics 49
Antialiasing (3) Pre-filtering Filter before sampling- determine pixels from the continuous signal Disadvantage: percent calculation introduces complexity Post-filtering Filter after sampling- determine e pixels from the discreet samples of the continuous signal 01074410 / 13016218 Computer Graphics 50
Antialiasing (4) Supersampling (or Post-filtering) use multiple sample points across the finer grid to determine an appropriate intensity level for each screen pixel Area sampling (or Pre-filtering) by calculating the areas of overlap of each pixel with the objects to be displayed Pixel phasing Hardware approach by shifting the display location of pixel areas ( micropositioning iti i the electron beam in relation to object geometry) 01074410 / 13016218 Computer Graphics 51
Supersampling p Straight-Line Segments Divide each pixel into a number of subpixels and count the number of subpixels that overlap the line path The intensity level for each pixel is then set to a value that is proportional to this subpixel count 1 2 2 3 1 01074410 / 13016218 Computer Graphics 52
Supersampling p Straight-Line Segments : Advantage Represent the line with finite width The number of possible intensity levels for each pixel is equal to the total number of subpixels within the pixel area 01074410 / 13016218 Computer Graphics 53
Supersampling p Straight-Line Segments : Advantage (2) Since a particular line might cross several different color areas We can average subpixel intensities to obtain pixel color settings Ex. 5 subpixels within a particular pixel area are determined to be inside a red line and the remaining 4 subpixels fall within a blue background pixel color = (5 red + 4 blue) / 9 01074410 / 13016218 Computer Graphics 54
Subpixel Weighting Mask By giving more weight to subpixels near the center of a pixel area Since these subpixels are to be more important in determining the overall intensity of a pixel Intensities calculated l for each of the 9 subpixels Center subpixel is weighted by a factor of 1/4 Top, bottom, and side subpixels are each of 1/8 Corner subpixels are each weighted by 1/16 01074410 / 13016218 Computer Graphics 55
Area Sampling Straight-Line Segments A method for estimating pixel overlap areas The pixel with grid coordinates (10, 20) is about 90% covered by the line area, so its intensity would be set to 90% of the maximum intensity Similarly (10, 21) would be set to 15% 01074410 / 13016218 Computer Graphics 56
Filtering Techniques A more accurate method for antialiasing lines Similar to those for applying a weighting mask, but now we integrate over the pixel surface to obtain the weighted average intensity 01074410 / 13016218 Computer Graphics 57
Pixel Phasing With the technique by moving (micropositioning) pixel positions closer to the line path The electron beam is typically shifted by ¼, ½, or ¾ of a pixel diameter to plot points closer to the true path of a line or object edge 01074410 / 13016218 Computer Graphics 58
Pixel Phasing (2) 01074410 / 13016218 Computer Graphics 59
Compensating for Line Intensity Differences The diagonal line is longer than the horizontal line by a factor of 22 By adjusting the intensity of each line according to its slope Horizontal and vertical lines would be displayed with the lowest intensity, while 45 lines would be given the highest intensity 01074410 / 13016218 Computer Graphics 60
Antialiasing Area Boundaries Smooth area boundaries by shifting pixel positions Adjust pixel intensity at a boundary according to the percent of the interior Adjustments, based on the percent of pixel area coverage 01074410 / 13016218 Computer Graphics 61
Antialiasing Area Boundaries (2) Supersampling methods Along the two scan lines, 3 of the subpixel areas are inside the boundary So we set the pixel intensity at 75% 01074410 / 13016218 Computer Graphics 62
Antialiasing Area Boundaries (3) Determining the percentage of pixel area within a fill region By Pitteway and Watkinson, based on the midpoint line algorithm 01074410 / 13016218 Computer Graphics 63
Overlap Area of the Pixel Parameter p y - y mid = p = [m(x k + 1) + b] (y k +0.5) + (1 m) Pixel at y k is nearer if p < 1 m, and at y k + 1 is nearer if p > 1 m The interior part of the pixel area = m x k + b y k + 0.5 By evaluating p, we also determine the percentage of area coverage for the current pixel 01074410 / 13016218 Computer Graphics 64
OpenGL Antialiasing Functions To activate the antialiasing routines glenable (primitivetype); where primitivetype is GL_POINT_SMOOTH, GL_LINE_SMOOTH, or GL_POLYGON_SMOOTH Color-blending operations glenable (GL _ BLEND); glblendfunc (GL _ SRC_ ALPHA, GL_ ONE_ MINUS_ SRC_ ALPHA); 01074410 / 13016218 Computer Graphics 65
End of Chapter 4 01074410 / 13016218 Computer Graphics 68