CS488. More Geometric Transformations, Object Hierarchies, and some Fonts. Luc RENAMBOT

Transcription

1 CS488 More Geometric Transformations, Object Hierarchies, and some Fonts Luc RENAMBOT 1

2 Previous Lectures Frame buffers Drawing a line (Midpoint Line Algorithm) Polygon Filling (Edge-table algorithm) Line Clipping (Cohen-Sutherland algorithm) Polygon Clipping Circles Geometric Transformations More Transformations 2

3 Transformations Last time we talked about 2D and 3D transformations and how those transformations affect objects in the scene Today we will talk more about this, and discuss how polygons are usually formed into hierarchies of more meaningful objects We will also briefly discuss how fonts are handled 3

4 Changing Coordinate Systems Last time we talked about transforms in terms of an object (polygon, line, point) in the same coordinate system of the world, that is (0,0) for the object is the same as (0,0) for the world An alternative way is for each object to have its own local coordinate system separate from all of the other objects and the world coordinate system 4

5 Local Coordinates This allows each object to be created separately and then added into the world, using transformations to place the object at the appropriate point Useful when you build larger objects out of reusable smaller objects 5

6 Example (1,4) (3,4) (-1,1) (1,1) (1,2) (3,2) (-1,-1) (1,-1) Square of width 2, height 2 6

7 Example Rotation 45 deg Scaling (2,2) 7

8 Example (2,2) (0,0) Translation (2,2) 8

9 Design When we design the object we place the center of rotation/scaling where we wish it to be. For a wheel the center of rotation would be where the axle is to be attached, for a hinged gate the center would be at the hinge. Each object must then be translated/rotated/scaled (from its local coordinate system) to place it at the proper location in the world (in the world coordinate system) 9

10 Example Say we are drawing an automobile and we want to draw the 4 tires. We can either draw each of the 4 tires independently at the appropriate location, or draw the same tire centered at its origin 4 times, and each time move it to the appropriate location in the world 10

11 OpenGL Example Create a solar system with a single sun and a single planet in orbit about it Simplifications circular orbit plane of the solar system: Y=0 plane Sun at 0,0,0 and sphere of radius 1 Planet a radius of 0.2 and orbits at a radius of 2 The planet rotates about its axis once per day The planet revolves around the sun once each year 11

12 Code glloadidentity(); //reset the matrix to the identity matrix glpushmatrix(); drawsphere(1.0) // user defined function to draw the sun glrotatef(yearpercentage, 0.0, 1.0, 0.0); gltranslatef(2.0, 0.0, 0.0); glrotatef(daypercentage, 0.0, 1.0, 0.0); drawsphere(0.2) // user defined function to draw the planet glpopmatrix(); 12

13 Single Coordinate System If you think about the single coordinate system then the operations on the matrix are done in the REVERSE order from which they are called: Initially the transformation matrix is the identity matrix The sun is drawn as a circle with radius 1 at (0,0,0) The planet is drawn as a circle with radius 0.2 at (0,0,0) The planet is rotated about the Y-axis by the percentage of day that has passed. Since the planet is still at the origin this rotates the planet about its center. The planet is translated 2 units on the X-axis moving its center to (2, 0, 0) The planet is rotated about the Y-axis by the percentage of year that has passed. Since the planet is no longer at the origin it rotates about the origin at a radius of 2 13

14 Local Coordinate System If you think about each object having its own coordinate system then the operations on the matrix are done in the SAME order as they are called: Initially the transformation matrix is the identity matrix The sun is drawn as a circle with radius 1 at (0,0,0) The planet is rotated about its Y-axis by the percentage of year that has passed turning its coordinate system in the process The planet is translated 2 units on its now rotated X-axis to its position in orbit The planet is rotated about its Y-axis by the percentage of day that has passed. Since the planet is still at (0,0,0) by its coordinate system, it rotates about its center. The planet is drawn as a circle with radius

15 Example Say you have three polygonal drawing functions available to you: Draw a square centered at the origin with sides of length 1 Draw a circle centered at the origin with diameter of length 1 Draw a equilateral triangle with the center of its base at the origin with sides of length 1 How can I draw the following scene? 15

16 Object Hierarchies Single polygons are generally too small to be of interest Its hard to think of a single polygon as an 'object' unless you are writing Tetris(tm) It is more convenient to think of objects which are a collection of polygons forming a recognizable shape: a car, a house This object can then be moved/rotated/scaled as a single entity, at least at the conceptual level 16

17 Object Hierarchies Creating an object polygon by polygon is very slow when you want to create a very large complex object It does give you much more control over the object than creating it from higher-level primitives (cube, cone, sphere) 17

18 OpenInventor Silicon Graphics (SGI) library OpenInventor(tm) sits on top of OpenGL Allows higher-level objects to be created File format and runtime environment 18

19 Example Model: a tree Constructed from a cube and a cone Constructed from triangular polygons 19

20 With primitives #Inventor V2.1 ascii Separator { Separator { Translation { translation } Material { diffusecolor } Cube { width 0.75 height 1.75 depth 0.75 } } Separator { Translation { translation } Material { diffusecolor } Cone { bottomradius 1.4 height 4.3 } 20

21 With polygons (1) #Inventor V2.1 ascii Separator { Separator { Material { diffusecolor } Separator { IndexedTriangleStripSet { vertexproperty VertexProperty { vertex [ , , , , , e-08, , , , e , , , , e-08, , , , ] } normal [ , , , , e-08, , , , e , , , , e-08, , , , ] materialbinding OVERALL normalbinding PER_VERTEX_INDEXED 21

22 With polygons (2) } } } coordindex [ 16, 0, 17, 2, 3, -1, 3, 4, 17, 5, 6, -1, 6, 7, 17, 8, 9, -1, 9, 10, 17, 11, 12, -1, 12, 13, 17, 14, 15, -1, 16, 17, 15, -1, 1, 1, 0, 2, -1, 1, 1, 2, 3, -1, 1, 1, 3, 4, -1, 1, 1, 4, 5, -1, 1, 1, 5, 6, -1, 1, 1, 6, 7, -1, 1, 1, 7, 8, -1, 1, 1, 8, 9, -1, 1, 1, 9, 10, -1, 1, 1, 10, 11, -1, 1, 1, 11, 12, -1, 1, 1, 12, 13, -1, 1, 1, 13, 14, -1, 1, 1, 14, 15, -1, 1, 1, 15, 16, -1, 1, 1, 16, 0, -1 ] normalindex [ 16, 16, 16, 16, 16, -1, 16, 16, 16, 16, 16, -1, 16, 16, 16, 16, 16, -1, 16, 16, 16, 16, 16, -1, 16, 16, 16, 16, 16, -1, 16, 16, 16, -1, 15, 0, 0, 1, -1, 0, 1, 1, 2, -1, 1, 2, 2, 3, -1, 2, 3, 3, 4, -1, 3, 4, 4, 5, -1, 4, 5, 5, 6, -1, 5, 6, 6, 7, -1, 6, 7, 7, 8, -1, 7, 8, 8, 9, -1, 8, 9, 9, 10, -1, 9, 10, 10, 11, -1, 10, 11, 11, 12, -1, 11, 12, 12, 13, -1, 12, 13, 13, 14, -1, 13, 14, 14, 15, -1, 14, 15, 15, 0, -1 ] } Material { diffusecolor } IndexedTriangleStripSet { vertexproperty VertexProperty { vertex [ , , , , , , , ] normal [ 0 0 1, 0 0-1, , 1 0 0, 0 1 0, ] texcoord [ ] orderedrgba [ ] materialbinding OVERALL normalbinding PER_VERTEX_INDEXED } } coordindex [ 5, 3, 7, 1, -1, 2, 4, 0, 6, -1, 5, 4, 3, 2, -1, 1, 0, 7, 6, -1, 7, 6, 5, 4, -1, 3, 2, 1, 0, -1 ] normalindex [ 5, 5, 5, 5, -1, 4, 4, 4, 4, -1, 3, 3, 3, 3, -1, 2, 2, 2, 2, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, -1 ] 22

23 Polygons Triangular polygons are often used instead of 4-sided ones because the 3 vertices in the triangle are guaranteed to form a plane, while the 4 vertices of a 4-sided polygon may not all fall in the same plane which may cause problems later on. 23

24 Hierarchies Hierarchies are typically stored as Directed Acyclic Graphs (DAG) They are trees where a node can have multiple parents as long as no cycle is generated. 24

25 Hierarchies Hierarchies store all information necessary to draw an object: Polygon information Material information Transformation information An object hierarchy gives a high degree of encapsulation 25

26 Hierarchies Hierarchies are useful when you want to be able to manipulate an object on multiple levels With an arm you may want to rotate the entire arm about the shoulder, or just the lower arm about the elbow, or just the wrist or just a finger. If you rotate the entire arm then you want the rest of the arm parts to follow along as though they were joined like a real arm - if you rotate the arm then the elbow should come along for the ride With a car the wheels should rotate but if the car body is moving then the wheels should also be moving the same amount 26

27 Example 27

28 Inheritance An object hierarchy allows inheritance Attributes to be set once then used by multiple sub-objects. For example, at the top of the hierarchy the object could be set to draw only as a wireframe, or with different lighting models, or different colors, or different texture maps. This would then be inherited by the sub-objects and not have to be explicitly set each of them 28

29 Benefits An object hierarchy gives a high degree of encapsulation Hierarchies increase modularity Hierarchies decrease storage space Hierarchies make it easy to propagate changes 29

30 Exercise How can I redraw the house and tree scene to make better use of objects? 30

31 Font Text is handled in one of two ways Using a bitmap for each character in the font Using lines / polygons for each character in the font 31

32 Bitmap Font Rectangular array of 0s and 1s A 32

33 Bitmap Font Need a set of bitmaps for each size and style of font 2D only Always aligned with the screen Dealt with specially while manipulating the frame buffer Fast 33

34 Polygonal Font Re-scalable so that the definition can generate a 'smooth' character of any size Can be either 2D or 3D Can be rotated Treated like any other line/ polygon to be displayed Slower 34

35 OpenGL Fonts OpenGL provides minimal font support glutbitmapcharacter glutstrokecharacter Fortunately there are free 3D fonts available, such freetype fonts and libraries 35

36 Bitmap OpenGL Bitmap void glutbitmapcharacter(void *font, int character) GLUT_BITMAP_8_BY_13 GLUT_BITMAP_9_BY_15 GLUT_BITMAP_TIMES_ROMAN_10 GLUT_BITMAP_TIMES_ROMAN_24 GLUT_BITMAP_HELVETICA_10 GLUT_BITMAP_HELVETICA_12 GLUT_BITMAP_HELVETICA_18 Ex: glutbitmapcharacter(glut_helvetica_18,'3'); Position in the frame buffer void glrasterpos2f(float x, float y); 36

37 3D Font OpenGL Drawn with lines Controlled by function gllinewidth Stroke void glutstrokecharacter(void *font, int character) GLUT_STROKE_ROMAN GLUT_STROKE_MONO_ROMAN Ex: glutstrokecharacter(glut_helvetica_18,'3') int glutstrokewidth(void *font, int character); Width of a character 37

38 Coming Next Time 3D Graphics More Matrices... 38