Graphics Output Primitives Hearn & Baker Chapter 3. Some slides are taken from Robert Thomsons notes.

Transcription

1 Graphics Output Primitives Hearn & Baker Chapter 3 Some slides are taken from Robert Thomsons notes.

2 OVERVIEW Coordinate reference frames OpenGL Point & Line functions Line drawing algorithms Curve drawing algorithms Fill-area primitives Pixel-array primitives Character primitives Picture Partitioning

3 Basic Elements Three basic elements Scalars Vectors Points Develop mathematical operations among them Define basic primitives: Points Line segments

4 Basic Elements Points are associated with locations in space Vectors have magnitude and direction represent displacements between points, or directions Points, vectors, and operators that combine them are the common tools for solving many geometric problems that arise in Geometric Modeling, Computer Graphics, Animation, Visualization, and Computational Geometry.

5 3.1 COORDINATE REFERENCE FRAMES To describe a picture, we first decide upon A convenient Cartesian coordinate system, called the world-coordinate reference frame, which could be either 2D or 3D. We then describe the objects in our picture by giving their geometric specifications in terms of positions in world coordinates. e.g., we define a straight-line segment with two endpoint positions, and a polygon is specified with a set of positions for its vertices. These coordinate positions are stored in the scene description along with other info about the objects, such as their color and their coordinate extents coordinate extents are the minimum and maximum x, y, and z values for each object. A set of coordinate extents is also described as a bounding box for an object. For a 2D figure, the coordinate extents are sometimes called its bounding rectangle.

6 3.1 COORDINATE REFERENCE FRAMES Objects are then displayed by passing the scene description to the viewing routines which identify visible surfaces and map the objects to the frame buffer positions and then on the video monitor. The scan-conversion algorithm stores info about the scene, such as color values, at the appropriate locations in the frame buffer, and then the scene is displayed on the output device. locations on a video monitor are referenced in integer screen coordinates, which correspond to the integer pixel positions in the frame buffer.

7 3.1 COORDINATE REFERENCE FRAMES Scan-line algorithms for the graphics primitives use the coordinate descriptions to determine the locations of pixels E.g., given the endpoint coordinates for a line segment, a display algorithm must calculate the positions for those pixels that lie along the line path between the endpoints. Since a pixel position occupies a finite area of the screen the finite size of a pixel must be taken into account by the implementation algorithms. for the present, we assume that each integer screen position references the centre of a pixel area.

8 3.1 COORDINATE REFERENCE FRAMES Once pixel positions have been identified the color values must be stored in the frame buffer Assume we have available a low-level procedure of the form setpixel (x, y); stores the current color setting into the frame buffer at integer position (x, y), relative to the position of the screen-coordinate origin getpixel (x, y, color); retrieves the current frame-buffer setting for a pixel location; parameter color receives an integer value corresponding to the combined RGB bit codes stored for the specified pixel at position (x,y). additional screen-coordinate information is needed for 3D scenes. For a two-dimensional scene, all depth values are 0.

9 3.1 Absolute and Relative Coordinate Specifications So far, the coordinate references discussed are given as absolute coordinate values values are actual positions wrt origin of current coordinate system some graphics packages also allow positions to be specified using relative coordinates as an offset from the last position that was referenced (called the current position)

10 Specifying A 2D World-coordinate Reference Frame in OpenGL World-coordinate limits for a display window, as specified in the glortho2d function. gluortho2d function specifies an orthogonal projection, we need also to be sure that the coordinate values are placed in the OpenGL projection matrix. In addition, we could assign the identity matrix as the projection matrix before defining the world-coordinate range. This would ensure that the coordinate values were not accumulated with any values we may have previously set for the projection matrix. glmatrixmode (GL_PROJECTION); glloadidentity ( ); glu0rtho2d (xmin, xmax, ymin, ymax); The display window will then be referenced by coordinates (xmin, ymin) at the lower-left corner and by coordinates (xmax, ymax) at the upper-right corner, as shown in Fig. 3-2.

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12 3-3 OpenGL POINT FUNCTIONS To specify the geometry of a point, we simply give a coordinate position in the world reference frame. Then along with other geometric descriptions this data is passed to the viewing routines. Unless we specify other attribute values, OpenGL primitives are displayed with a default size and color. The default color for primitives is white and the default point size is equal to the size of one screen pixel.

13 3-3 OpenGL POINT FUNCTIONS A glvertex function must be placed between a glbegin function and a glend function. The argument of the glbegin function is used to identify the kind of output primitive that is to be displayed For point plotting, the argument of the glbegin function is the symbolic constant GL_POINTS. and glend takes no arguments. glbegin (GL_POINTS); glvertex* ( ); glend ( ) ;

14 3-3 OpenGL POINT FUNCTIONS glvertex* ( ); state the coordinate values for a single position where the asterisk (*) indicates that suffix codes are required for this function. These suffix codes are used to identify the spatial dimension, 2, 3, or 4 (indicates a scaling factor for the Cartesian-coordinate values.) the numerical data type i (integer), s (short), f (float), and d (double) and a possible vector form for the coordinate specification append a third suffix code: v (for "vector"). the glvertex function is used in OpenGL to specify coordinates for any point position. In this way, a single function is used for point, line, and polygon specifications

15 3-3 OpenGL POINT FUNCTIONS. glbegin (GL_POINTS); glvertex2i (50, 100); glvertex2i (75, 150); glvertex2i (100, 200); g1end ( ) ; Alternatively, we could specify the coordinate values for the preceding points in arrays such as int point1 [ ] = {50, 100}; int point2 [ ] = {75, 150}; int point3 [ ] = {100, 200}; and call the OpenGL functions for plotting the three points as glbegin (GL_POINTS); glvertex2iv (pointl); glvertex2iv (point2); glvertex2iv (point3); glend ( ) ;

16 3-3 OpenGL POINT FUNCTIONS. class wcpt2d { public: GLfloat x, y; }; Using this class definition, we could specify a 2D, worldcoordinate point position with the statements wcpt2d pointpos; pointpos.x = ; pointpos.y = 45.30; glbegin (GL_POINTS); glvertex2f (pointpos.x, pointpos.y); glend ( )

17 3-4 OpenGL LINE FUNCTIONS now we use a symbolic constant as the argument for the glbegin function that interprets a list of positions as the endpoint coordinates for line segments. A set of straight-line segments between each successive pair of endpoints in a list is generated using the primitive line constant GL_LINES glbegin (GL_LINES): glvertex2iv(pl); glvertex2iv(p2); glvertex2iv(p3); glvertex2iv(p4); glvertex2iv(p5); glend ( ); Nothing is displayed if we do not list at least two coordinate positions p2 p3 p4 pl

18 3-4 OpenGL LINE FUNCTIONS. glbegin (GL_LINE_STRIP); glvertex2iv (pl); glvertex2iv (p2); glvertex2iv (p3); glvertex2iv (p4); p3 glvertex2iv (p5); p5 pl glend ( ) The first line segment in the polyline is displayed between the first endpoint and the second endpoint; the second line segment is between the second and third endpoints; and so forth, up to the last line endpoint. p2 p4

19 3-4 OpenGL LINE FUNCTIONS gibegin (GL_LINE_LOOP); glvertex2iv (pl); glvertex2iv (p2); glvertex2iv (p3); glvertex2iv (p4); glvertex2iv (p5); glend ( ) ; produces a closed polyline. the last coordinate endpoint in the sequence is connected to the first coordinate endpoint of the polyline. p5 p2 p3 p4 pl

20 3-5 LINE-DRAWING ALGORITHMS A straight-line segment in a scene is defined by the coordinate positions for the endpoints of the segment. 1. To display the line on a raster monitor, the graphics system must first project the endpoints to integer screen coordinates and determine the nearest pixel positions along the line path between the two endpoints. 2. Then the line color is loaded into the frame buffer at the corresponding pixel coordinates. 3. Reading from the frame buffer, the video controller plots the screen pixels. This process digitizes the line into a set of discrete integer positions that, in general, only approximates the actual line path.

21 3-5 LINE-DRAWING ALGORITHMS On raster systems, lines are plotted with pixels, and step sizes in the horizontal and vertical directions are constrained by pixel separations. That is, we must "sample" a line at discrete positions and determine the nearest pixel to the line at sampled position. Sampling is measuring the values of the function at equal intervals Idea: A line is sampled at unit intervals in one coordinate and the corresponding integer values nearest the line path are determined for the other coordinate.

22 Towards the Ideal Line We can only do a discrete approximation Illuminate pixels as close to the true path as possible, consider bi-level display only Pixels are either lit or not lit In the raster line alg., we sample at unit intervals and determine the closest pixel position to the specified line path at each step

23 What is an ideal line Must appear straight and continuous Only possible with axis-aligned and 45 o lines Must interpolate both defining end points Must have uniform density and intensity Consistent within a line and over all lines What about anti-aliasing? Aliasing is the jagged edges on curves and diagonal lines in a bitmap image. Anti-aliasing is the process of smoothing out those jaggies. Graphics software programs have options for anti-aliasing text and graphics. Enlarging a bitmap image accentuates the effect of aliasing. Must be efficient, drawn quickly Lots of them are required

24 Simple Line The Cartesian slope-intercept equation for a straight line is : y = mx + b with m as the slope of the line and b as the y intercept. Simple approach: increment x, solve for y

25 Line-Drawing Algorithms: DDA Bresenham s Midpoint Algorithm

26 Algorithms for displaying lines are based on the Cartesian slope-intercept equation y = m.x + b where m and b can be calculated from the line endpoints: m = (y1-y0) / (x1-x0) b = y0 - m. x0 For any x interval x along a line the corresponding y = m.x y interval y 1 y 0 x 0 x 1

27 Simple Line Based on slope-intercept algorithm from algebra: y = mx + b Simple approach: increment x, solve for y Floating point arithmetic required

28 Does it Work? It works for lines with a slope of 1 or less, but doesn t work well for lines with slope greater than 1 lines become more discontinuous in appearance and we must add more than 1 pixel per column to make it work. Solution? - use symmetry.

29 Modify algorithm per octant OR, increment along x-axis if dy<dx else increment along y-axis

30 DDA Algorithm The digital differential analyser (DDA) is a scan-conversion line algorithm based on using x or y. A line is sampled at unit intervals in one coordinate and the corresponding integer values nearest the line path are determined for the other coordinate.

31 Line with positive slope If m<=1, Sample at unit x intervals (dx=1) Compute successive y values as y k+1 =y k +m 0<=k<=x end -x 0 Increment k by 1 for each step Round y to nearest integer value. If m>1, Sample at unit y intervals (dy=1) Compute successive x values as x k+1 =x k +1/m 0<=k<=y end -y 0 Increment k by 1 for each step Round x to nearest integer value.

32 inline int round (const float a) { return int (a + 0.5); } void linedda (int x0, int y0, int xend, int yend) { int dx = xend - x0, dy = yend - y0, steps, k; float xincrement, yincrement, x = x0, y = y0; if (fabs (dx) > fabs (dy)) steps = fabs (dx); else steps = fabs (dy); xincrement = float (dx) / float (steps); yincrement = float (dy) / float (steps); } setpixel (round (x), round (y)); for (k = 0; k < steps; k++) { x += xincrement; y += yincrement; setpixel (round (x), round (y)); }

33 DDA algorithm Need a lot of floating point arithmetic. 2 round s and 2 adds per pixel. Is there a simpler way? Can we use only integer arithmetic? Easier to implement in hardware.

34 Bresenham's line algorithm Accurate and efficient Uses only incremental integer calculations The method is described for a line segment with a positive slope less than one The method generalizes to line segments of other slopes by considering the symmetry between the various octants and quadrants of the xy plane

35 Bresenham's line algorithm Specified line path Decide what is the next pixel position (11,11) or (11,12)

36 Illustrating Bresenham s Approach y k+3 y k+2 y=mx+b For the pixel position x k+1 =x k +1, which one we should choose: (x k+1,y k ) or (x k+1, y k+1 ) y k+1 y k x k x k+1 x k+2 x k+3

37 Bresenham s Approach y k+1 y y k d upper d lower y=m(x k + 1)+b d lower =y-y k =m(x k + 1)+b-y k x k+1 d lower - d upper = 2m(x k + 1)-2y k +2b-1 d upper =(y k +1)-y = y k +1 -m(x k + 1)-b Rearrange it to have integer calculations: m=δy/δx Decision parameter: p k = Δx(d lower - d upper )=2Δy.x k - 2Δx. y k + c

38 The Decision Parameter Decision parameter: p k = Δx(d lower - d upper )=2Δy.x k - 2Δx. y k + c p k has the same sign with d lower - d upper since Δx>0. c is constant and has the value c= 2Δy + Δx(2b-1) c is independent of the pixel positions and is eliminated from decision parameter p k. If d lower < d upper then p k is negative. Plot the lower pixel (East) Otherwise Plot the upper pixel (North East)

39 At step k+1 Succesive decision parameter p k+1 = 2Δy.x k+1-2δx. y k+1 + c Subtracting two subsequent decision parameters yields: p k+1 -p k = 2Δy.(x k+1 -x k ) - 2Δx. (y k+1 -y k ) x k+1 =x k +1 so p k+1 = p k + 2Δy - 2Δx. (y k+1 -y k ) y k+1 -y k is either 0 or 1 depending on the sign of p k First parameter p 0 p 0 =2 Δy - Δx

40 Bresenham's Line-Drawing Algorithm for I m I < 1 1. Input the twoline endpoints and store the left endpoint in (x 0,y 0 ). 2. Load (x 0,y 0 ) into the frame buffer; that is, plot the first point. 3. Calculate constants Δx, Δy, 2Δy, and 2Δy - 2Δx, and obtain the starting value for the decision parameter as p 0 =2 Δy - Δx 4. At each x k along the line, starting at k = 0, perform the following test: If p k < 0, the next point to plot is (x k+1, y k ) and p k+1 =p k + 2Δy Otherwise, the next point to plot is (x k+1, y k+1 ) and p k+1 =p k + 2Δy - 2Δx 5. Repeat step 4 Δx -1 times.

41 Trivial Situations: Do not need Bresenham m 0 horizontalline m 1 line y x m vertical line

42 Example Draw the line with endpoints (20,10) and (30, 18). Δx=30-20=10, Δy=18-10=8, p 0 = 2Δy Δx=16-10=6 2Δy=16, and 2Δy - 2Δx=-4 Plot the initial position at (20,10), then

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44 Example Line end points: Deltas: dx 4; dy ( x y ) (5,8); x, y ), 0 0 ( (9,11) initially p(5, 8) 2( dy) -( dx) p 2 NE

45 Graph

46 Continue the process

47 Graph

48 Graph

49 Graph

50 /* Bresenham line-drawing procedure for m < 1.0. */ void linebres (int x0, int y0, int xend, int yend) { int dx = fabs (xend - x0), dy = fabs(yend - y0); int x, y, p = 2 * dy - dx; int twody = 2 * dy, twodyminusdx = 2 * (dy - dx); } /* Determine which endpoint to use as start position. */ if (x0 > xend) { x = xend; y = yend; xend = x0; } else { x = x0; y = y0; } setpixel (x, y); while (x < xend) { x++; if (p < 0) p += twody; else { y++; p += twodyminusdx; } setpixel (x, y); }

51 Line-drawing algorithm should work in every octant, and special cases m<-1 m>1 0>m>-1 0<m<1 0<m<1 0>m>-1 m>1 m<-1

52 Simulating the Bresenham algorithm in drawing 8 radii on a circle of radius 20 Horizontal, vertical and 45 radii handled as special cases

53 Circle / Curve Drawing in OpenGL Routines for drawing circles or ellipses are not included in the OpenGL core library. Does include functions for displaying Bezier splines GLU (OpenGL Utility) library has some routines for drawing spheres, cylinders, B-splines. Rational B-splines can be used to display circles and ellipses. GLUT (OpenGL Utility Toolkit) has some routines to display 3D shapes such as cones, spheres All these discussed later

54 Another method: Approximate it using a polyline.

55 Scan Converting Circles ( x x c ) 2 ( y y c ) 2 R 2 y y c R 2 ( x x c ) 2 Explicit: y = f(x) y R x 2 2 We could draw a quarter circle by incrementing x from 0 to R in unit steps and solving for +y for each step. Method needs lots of computation, and gives non-uniform pixel spacing

56 Parametric: x y Scan Converting Circles Rcos Rsin Draw quarter circle by stepping through the angle from 0 to 90 -avoids large gaps but still unsatisfactory -How to set angular increment Computationally expensive trigonometric calculations

57 Scan Converting Circles Implicit: f(x,y) = x 2 +y 2 -R 2 If f(x,y) = 0 then it is on the circle. f(x,y) > 0 then it is outside the circle. f(x,y) < 0 then it is inside the circle. Try to adapt the Bresenham midpoint approach Again, exploit symmetries

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59 Generalising the Bresenham midpoint approach Set up decision parameters for finding the closest pixel to the cırcumference at each sampling step Avoid square root calculations by considering the squares of the pixel separation distances Use direct comparison without squaring. Adapt the midpoint test idea: test the halfway position between pixels to determine if this midpoint is inside or outside the curve This gives the midpoint algorithm for circles Can be adapted to other curves: conic sections

60 Eight-way Symmetry - only one octant s calculation needed

61 The 2 nd Octant is a good arc to draw It is a well-defined function in this domain single-valued no vertical tangents: slope 1 Lends itself to the midpoint approach only need consider E or SE Implicit formulation F(x,y) = For (x,y) on the circle, F(x,y) = 0 x 2 + y 2 r 2 F(x,y) > 0 (x,y) Outside F(x,y) < 0 (x,y) Inside

62 Choose E or SE Decision variable d is x 2 + y 2 r 2 Then d = F(M) 0 SE Or d = F(M) < 0 E

63 F (M) 0 SE current pixel ideal curve E M SE

64 F (M) < 0 E E ideal curve M SE

65 Decision Variable p As in the Bresenham line algorithm we use a decision variable to direct the selection of pixels. Use the implicit form of the circle equation p = F (M ) = x 2 + y 2 r 2

66 1 2 Midpoint coordinates are ( x k 1, yk )

67 Assuming we have just plotted point at (xk,yk) we determine whether move E or SE by evaluating the circle function at the midpoint between the two candidate pixel positions p k F ( x circ k ( x k 1) 2 1, y ( y k k 1 ) 2 1 ) 2 2 r 2 pk is the decision variable if pk <0 the midpoint is inside the circle Thus the pixel above the midpoint is closer to the ideal circle, and we select pixel on scan line yk. i.e. Go E

68 If pk >0 the midpoint is outside the circle. Thus the pixel below the midpoint is closer to the ideal circle, and we select pixel on scan line yk-1. i.e. Go SE Calculate successive decision parameter values p by incremental calculations. p k1 F [( x circ k ( x k1 1) 1] 1, 2 y k 1 ( y k1 1 ) 2 1 ) 2 2 r 2

69 recursive definition for successive decision parameter values p 1 ) ( ) ( 1) 2( ) 2 1 ( 1] 1) [( ) 2 1 1, ( k k k k k k k k k k k circ k y y y y x p p r y x y x F p Where yk+1 = yk if p<0 (move E) yk+1 = yk-1 if p>0 (move SE) yk+1 and xk+1 can also be defined recursively

70 Initialisation x 0 = 0, y 0 = r Initial decision variable found by evaluating circle function at first midpoint test position p F (1, r 1 0 circ 1 ( r 5 4 r 1 ) 2 ) 2 For integer radius r p 0 can be rounded to p 0 =1-r since all increments are integer. 2 r 2

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72 Midpoint Circle Algorithm (cont.)

73 r=10 Example

74 Conic Sections A conic section, or conic, is any figure that can be formed by slicing a double cone with a plane Parabola Circle Ellipse Hyperbola

75 General equation of a Conic Section Ax 2 By 2 Cxy Dx Ey F 0 Parabola: A = 0 OR B = 0 Circle: Ellipse: Hyperbola: A = B AB, but both have the same sign A and B have different signs

76 Ellipses F1 d1 F2 d2 P = (x,y) Ellipse generated about foci F1 and F2 d1 + d2 = constant

77 Scan Converting Ellipses F x y b x a y a b (, ) 0 b a a is the length of the semi-major axis along the x axis. b is the length of the semi-minor axis along the y axis. The midpoint algorithm can also be applied to ellipses. For simplicity, we draw only the arc of the ellipse that lies in the first quadrant, the other three quadrants can be drawn by symmetry

78 Regions

79 Region 1

80 Region 2

81 Fill area : an area that is filled with solid colour or pattern

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83 Identifying a concave polygon has at least one interior angle >180 degrees extensions of some edges will intersect other edges One test: Express each polygon edge as a vector, with a consistent orientation. Can then calculate cross-products of adjacent edges

84 Identifying a concave polygon When polygon edges are oriented with an anticlockwise sense z coordinate of the cross product at convex vertex has positive sign concave vertex gives negative sign

85 Normals Every plane has a vector n normal (perpendicular, orthogonal) to it n = u x v (vector cross product) u v P x y y x z x x z y z z y v u v u v u v u v u v u v u

86 Vector method for splitting concave polygons E 5 E 6 E 1 E 2 E E 4 E 1 =(1,0,0) E 2 =(1,1,0) E 3 =(1,-1,0) E 4 =(0,2,0) E 5 =(-3,0,0) E 6 =(0,-2,0) All z components have 0 value. Cross product of two vectors E j xe k is perpendicular to them with z component E jx E ky -E kx E jy

87 Example continued E 6 E 5 E 4 E 1 xe 2 = (0,0,1) E 2 xe 3 = (0,0,-2) E 3 xe 4 = (0,0,2) E 4 xe 5 = (0,0,6) E 5 xe 6 = (0,0,6) E 6 xe 1 = (0,0,2) E 2 E 3 E Since E 2 xe 3 has negative sign, split the polygonalong the line of vector E 2

88 Rotational method Rotate the polygon so that each vertex in turn is at coordinate origin. If following vertex is below the x axis, polygon is concave. Split the polygon by x axis.

89 E 5 E 6 E 4 E 2 E 3 E 1

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92 Inside-Outside? nonzero winding-number rule A winding number is an attribute of a point with respect to a polygon that tells us how many times the polygon encloses (or wraps around) the point. It is an integer, greater than or equal to 0. Regions of winding number 0 (unenclosed) are obviously outside the polygon, and regions of winding number 1 (simply enclosed) are obviously inside the polygon. Initially 0 +1: edge crossing the line from right to left -1: left to right

93 Winding Number Count clockwise encirclements of point winding number = 1 winding number = 2 Alternate definition of inside: inside if winding number 0

94 Polygon tables store descriptions of polygon geometry and topology, and surface parameters: colour, transparency, light-reflection organise in 2 groups geometric data attribute data

95 Polygon Tables: Geometric data Data can be used for consistency checking Additional geometric data stored: slopes, bounding boxes

96 Shared Edges Vertex lists will draw filled polygons correctly but if we draw the polygon by its edges, shared edges are drawn twice Can store mesh by edge list

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98 Inward and Outward Facing Polygons The order {v 1, v 6, v 7 } and {v 6, v 7, v 1 } are equivalent in that the same polygon will be rendered by OpenGL but the order {v 1, v 7, v 6 } is different The first two describe outwardly facing polygons Use the right-hand rule = counter-clockwise encirclement of outward-pointing normal OpenGL can treat inward and outward facing polygons differently

99 OpenGL Primitives GL_POLYGON GL_TRIANGLES GL_TRIANGLE_STRIP GL_TRIANGLE_FAN GL_QUADS GL_QUADSTRIP

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106 Modelling a Cube 3.17 : OpenGL vertex arrays Model a color cube for rotating cube program Define global arrays for vertices and colors GLfloat vertices[][3] = {{-1.0,-1.0,-1.0},{1.0,-1.0,-1.0}, {1.0,1.0,-1.0}, {-1.0,1.0,-1.0}, {-1.0,-1.0,1.0}, {1.0,-1.0,1.0}, {1.0,1.0,1.0}, {-1.0,1.0,1.0}}; GLfloat colors[][3] = {{0.0,0.0,0.0},{1.0,0.0,0.0}, {1.0,1.0,0.0}, {0.0,1.0,0.0}, {0.0,0.0,1.0}, {1.0,0.0,1.0}, {1.0,1.0,1.0}, {0.0,1.0,1.0}};

107 Drawing a polygon from a list of indices Draw a quadrilateral from a list of indices into the array vertices and use color corresponding to first index void polygon(int a, int b, int c, int d) { glbegin(gl_polygon); glcolor3fv(colors[a]); glvertex3fv(vertices[a]); glvertex3fv(vertices[b]); glvertex3fv(vertices[c]); glvertex3fv(vertices[d]); glend(); }

108 Draw cube from faces void colorcube( ) { polygon(0,3,2,1); polygon(2,3,7,6); polygon(0,4,7,3); polygon(1,2,6,5); polygon(4,5,6,7); polygon(0,1,5,4); } Note that vertices are ordered so that we obtain correct outward facing normals 0 3

109 Efficiency The weakness of our approach is that we are building the model in the application and must do many function calls to draw the cube Drawing a cube by its faces in the most straight forward way requires 6 glbegin, 6 glend 6 glcolor 24 glvertex More if we use texture and lighting

110 Vertex Arrays OpenGL provides a facility called vertex arrays that allows us to store array data in the implementation Six types of arrays supported Vertices Colors Color indices Normals Texture coordinates Edge flags We will need only colors and vertices

111 Initialization Using the same color and vertex data, first we enable glenableclientstate(gl_color_array); glenableclientstate(gl_vertex_array); Identify location of arrays glvertexpointer(3, GL_FLOAT, 0, vertices); 3d arrays stored as floats data array data contiguous (offset) glcolorpointer(3, GL_FLOAT, 0, colors);

112 Mapping indices to faces Form an array of face indices GLubyte cubeindices[24] = {0,3,2,1,2,3,7,6 0,4,7,3,1,2,6,5,4,5,6,7,0,1,5,4}; Each successive four indices describe a face of the cube Draw through gldrawelements which replaces all glvertex and glcolor calls in the display callback

113 Drawing the cube Method 1: what to draw number of indices for(i=0; i<6; i++) gldrawelements(gl_polygon, 4, GL_UNSIGNED_BYTE, &cubeindices[4*i]); format of index data Method 2: start of index data gldrawelements(gl_quads, 24, GL_UNSIGNED_BYTE, cubeindices); Draws cube with 1 function call!!

114 OpenGL Character Functions Characters are defined as bitmap functions. Some predefined character sets are available in GLUT. Display a bitmap GLUT character with glutbitmapcharacter (font, character) Use either the ASCII code (i.e. 65) or the specific character (i.e. A ) Can select a fixed-width fonts GLUT_BITMAP_8_BY_13 or GLUT_BITMAP_9_BY_15 GLUT_BITMAP_TIMES_ROMAN_10

115 OpenGL Character Functions Define the lower left corner of the bitmap as current raster position. glrasterposition2i (x, y) for (k=0; k<36;k++) glutbitmapcharacter (GLUT_BITMAP_9_BY_15,text [k]); Characters in text array is displayed starting from position (x,y) with current color.

116 OpenGL Display Lists Structures for storing object descriptions Must define (name, create) Add contents Close Reference the list, with different display options In client-server environment, display list is placed on server Can be redisplayed without sending primitives over network each time

117 Display List Functions Creating a display list GLuint listid; void init() { } //generates a unique identifier glnewlist( listid, GL_COMPILE ); listid = glgenlists( 1 ); /* other OpenGL routines */ glendlist(); Call a created list void display() { } glcalllist( listid ); //executes the display list

118 Display Lists and State Most OpenGL functions can be put in display lists Can put one list in another State changes made inside a display list persist after the display list is executed

119 Hierarchy and Display Lists Consider model of a car - Create display list for chassis - Create display list for wheel glnewlist( CAR, GL_COMPILE ); glcalllist( CHASSIS ); gltranslatef( ); glcalllist( WHEEL ); gltranslatef( ); glcalllist( WHEEL ); glendlist();

120 Handling Input in OpenGL Input devices contain a trigger which can be used to send a signal to the operating system Button on mouse Pressing or releasing a key When triggered, input devices return information (their measure) to the system Mouse returns position information Keyboard returns ASCII code

121 Request Mode Input provided to program only when user triggers the device Typical of keyboard input Can erase (backspace), edit, correct until the enter (return) key (the trigger) is depressed

122 Event Mode Most systems have more than one input device, each of which can be triggered at an arbitrary time by a user Each trigger generates an event whose measure is put in an event queue which can be examined by the user program

123 GLUT Event Loop Recall that the last line in main.c for a program using GLUT must be glutmainloop(); which puts the program in an infinite event loop In each pass through the event loop, GLUT looks at the events in the queue for each event in the queue, GLUT executes the appropriate callback function if one is defined if no callback is defined for the event, the event is ignored

124 Event Types Window: resize, expose Mouse: click one or more buttons Motion: move mouse Keyboard: press or release a key Idle: nonevent Define what should be done if no other event is in queue

125 Callbacks Programming interface for event-driven input Define a callback function for each type of event the graphics system recognizes This user-supplied function is executed when the event occurs GLUT example: glutmousefunc(mymouse) mouse callback function

126 Interaction in OpenGL : callbacks Handling Input Events You can use these routines to register callback commands that are invoked when specified events occur. glutkeyboardfunc(void (*func)(unsigned char key, int x, int y)) and glutmousefunc(void (*func)(int button, int state, int x, int y)) allow you to link a keyboard key or a mouse button with a routine that's invoked when the key or mouse button is pressed or released. glutmotionfunc(void (*func)(int x, int y)) registers a routine to call back when the mouse is moved while a mouse button is also pressed. glutreshapefunc(void (*func)(int w, int h)) indicates what action should be taken when the window is resized.

127 The display callback The display callback is executed whenever GLUT determines that the window should be refreshed, for example When the window is first opened When the window is reshaped When the user program decides it wants to change the display In main.c glutdisplayfunc(mydisplay) identifies the function to be executed Every GLUT program must have a display callback

128 Display function After the window is created, but before you enter the main loop, you should register callback functions using the following routines. void glutdisplayfunc(void (*func)(void)); Specifies the function that's called whenever the contents of the window need to be redrawn. The contents of the window may need to be redrawn when the window is initially opened, when the window is popped and window damage is exposed, and when glutpostredisplay() is explicitly called.

129 Post redisplay void glutpostredisplay(void); Marks the current window as needing to be redrawn. At the next opportunity, the callback function registered by glutdisplayfunc() will be called. Many events may invoke the display callback function Can lead to multiple executions of the display callback on a single pass through the event loop We can avoid this problem by instead using glutpostredisplay(); which sets a flag. GLUT checks to see if the flag is set at the end of the event loop If set then the display callback function is executed

130 Keyboard function glutkeyboardfunc(void (*func)(unsigned char key, int x, int y)) Specifies the function, func, that's called when a key that generates an ASCII character is pressed. The key callback parameter is the generated ASCII value. The x and y callback parameters indicate the location of the mouse (in window-relative coordinates) when the key was pressed.

131 Mouse function void glutmousefunc(void (*func)(int button, int state, int x, int y)); Specifies the function, func, that's called when a mouse button is pressed or released. The button callback parameter is one of GLUT_LEFT_BUTTON, GLUT_MIDDLE_BUTTON, or GLUT_RIGHT_BUTTON. The state callback parameter is either GLUT_UP or GLUT_DOWN,depending upon whether the mouse has been released or pressed. The x and y callback parameters indicate the location (in window-relative coordinates) of the mouse when the event occurred.

132 Motion function void glutmotionfunc(void (*func)(int x, int y)); Specifies the function, func, that's called when the mouse pointer moves within the window while one or more mouse buttons is pressed. The x and y callback parameters indicate the location (in window-relative coordinates) of the mouse when the event occurred.

133 Reshape function void glutreshapefunc(void (*func)(int width, int height)); Specifies the function that's called whenever the window is resized or moved. The argument func is a pointer to a function that expects two arguments, the new width and height of the window. Typically, func calls glviewport(), so that the display is clipped to the new size, and it redefines the projection matrix so that the aspect ratio of the projected image matches the viewport, avoiding aspect ratio distortion. If glutreshapefunc() isn't called or is deregistered by passing NULL, a default reshape function is called, which calls glviewport(0, 0, width, height). Viewports are discussed in H&B Ch.6

134 Example: handling a mouse button press void mykeyboardfunc (unsigned char key, int x, int y) { switch (key) { case 'f': removefirstpoint(); glutpostredisplay(); break; } case 27: } exit(0); break; // Escape key

135 Example: handling a mouse button press // use left button presses place a control point. void mymousefunc( int button, int state, int x, int y ) { if ( button==glut_left_button && state==glut_down ) { float xpos = ((float)x)/((float)(windowwidth-1)); float ypos = ((float)y)/((float)(windowheight-1)); ypos = 1.0f-yPos; // Flip value since y position is from top row. } } addnewpoint( xpos, ypos ); glutpostredisplay();

136 Positioning The position in the screen window is usually measured in pixels with the origin at the top-left corner Consequence of refresh done from top to bottom OpenGL uses a world coordinate system with origin at the bottom left Must invert y coordinate returned by callback by height of window y = h y; (0,0) h w

137 Obtaining the window size To invert the y position we need the window height Height can change during program execution Track with a global variable New height returned to reshape callback

138 Terminating a program In our original programs, there was no way to terminate them through OpenGL We can use the simple mouse callback void mouse(int btn, int state, int x, int y) { if(btn==glut_right_button && state==glut_down) exit(0); }

139 Using the mouse position In the next example, we draw a small square at the location of the mouse each time the left mouse button is clicked This example does not use the display callback but one is required by GLUT; We can use the empty display callback function mydisplay(){}

140 Drawing squares at cursor location void mymouse(int btn, int state, int x, int y) { if(btn==glut_right_button && state==glut_down) exit(0); if(btn==glut_left_button && state==glut_down) drawsquare(x, y); } void drawsquare(int x, int y) { y=w-y; /* invert y position */ glcolor3ub( (char) rand()%256, (char) rand )%256, (char) rand()%256); /* a random color */ glbegin(gl_polygon); glvertex2f(x+size, y+size); glvertex2f(x-size, y+size); glvertex2f(x-size, y-size); glvertex2f(x+size, y-size); glend(); }