1. Vector Graphics Digital Multimedia Chap.4 2006. 4. 4 이병희 icebyung@hufs.ac.kr

2. 이병희 2 Vector Graphics  Vector Graphics Compact Scaleable Resolution-independent Easy to edit  Attractive for networked multimedia

3. 이병희 3 Coordinates and Vectors  Coordinates Image is stored as a rectangular array of pixels  Rectangular array of pixels, each pixel is identified by row and column numbers (r,c)  coordinates  Coordinates of pixels in an image must be integer values between zero and the horizontal or vertical Coordinate transformation  Coordinates in one system are transformed into a different one  Vector Specify a displacement by movements in x and y directions Displacement is also a pair of numbers P 2 - P 1 = (x 2 -x 1, y 2 -y 1 ), displacement (movement) from P 1 to P 2 P 2 - P 1 ≠ P 1 - P 2 P1P1 P2P2 P 2 -P 1 X 2 -X 1 Y 2 -Y 1

4. 이병희 4 Rendering  Represent lines, curves, shapes,... by parameters of their defining equations e.g. : equation of straight line y = mx + c, store m and c (or endpoints)  Compute pixels which must be set in order to draw the object Pixel ’ s coordinates are always integers Can ’ t set the value of just part of a pixel  The pixel image can only ever approximate the ideal mathematical object Result exhibit ‘ jaggies ’ or ‘ staircasing ’ Figure 4.4 Approximating a straight line

5. 이병희 5 Anti-aliasing  Rendering is sampling and reconstruction Abstract continuous line &c must be approximated by discrete pixels of finite size Jaggies are form of aliasing caused by undersampling  Anti-aliasing Anti-aliasing is used to reduce aliasing impact Mitigate effect by coloring pixels in shades of grey (for a black line), brightness varies according to extent of intersection with an idealized 1 pixel wide line Figure 4.6 Anti-aliased line

6. 이병희 6 Shapes  Drawing programs and vector graphics languages provide basic repertoire of shapes that can easily be represented mathematically Rectangles and squares Ellipses and circles Straight lines, polylines and polygons Smooth (B é zier) curves Shapes built up out of these elements can be filled with color, patterns or gradients polyline

7. 이병희 7 Carves  B é zier Curves A class of curve B é zier curves (smooth curves) completely specified by four points  2 endpoints (P 1, P 2 )  2 direction points (P 3, P 4 )  Sweep of the curve is determined by length and direction of lines from endpoints to direction points Constructing a B é zier curves  Figure 4.10 figure 4.8 Bézier Curves (p.92)

8. 이병희 8 Paths  B é zier curves can be combined to make elaborate curves and irregular shapes Joining two B é zier curves Path  Collection of lines and curves  Closed path joins up on itself, open path doesn ’ t Closed path Open path

9. 이병희 9 Stroke and Fill  Path is an abstract mathematical entity Path is infinitesimally thin Apply stroke to make path visible (like tracing with ink)  Specify width and color etc  Line cap : subtle feature of stroke (shape of end)  Butt cap, round cap, projecting cap Apply fill to closed path or shape (like coloring it in)  Specify color or a gradient or pattern  Gradients may be linear or radial figure 4.20 Gradient fills figure 4.22 pattern fills

10. 이병희 10 Transformations  The objects that make up a vector image are stored in the form of a few values  Manipulate vector objects in certain ways by changing stored values that describe them Translation (liner movement) Scaling Reflection Rotation Shearing (skewing) Original shapescalingreflectionrotationshearing

11. 이병희 11 3-D Graphics  3-D Vector Graphics Conceptually simple extension of 2-D  Add z-axis at right angles to x- and y-axes  Point is defined by (x, y, z) coordinates, vector is triple of values  3-D Rendering Start with mathematical model of objects in 3-D space, need a 2-D picture, usually in perspective Need to consider viewpoint ( or camera position) Need to consider lighting (position of light source)  Surface ’ s appearance (texture, diffuse … ) can be determine by position and lighting condition

12. 이병희 12 3D-Models  Three general approaches to modeling 3-D object Constructive solid geometry Free form modeling Procedural modeling  Constructive solid geometry Simplest approach Build 3-D models out of a few primitive objects such as cube, cylinder, sphere and pyramid Apply distortions such as squashing or stretching Combine objects using spatial equivalents of set operations  Union, intersection, difference differenceunionintersection

13. 이병희 13 3D-Models  Free form modeling Use representation of an object’s boundary surface to define it Build surfaces out of flat polygons or curved patches Construct surface as mesh of flat polygons Can generalize B é zier curves to 3-D surfaces Generate objects by sweeping 2-D cross section along a path  Extrusion and lathing  Procedural modeling Define an object by giving algorithm for constructing it Fractals  Exhibit same structure at all level of detail  Model landscape features, clouds Metaballs Figure 4.38 constructing a well-known fractal curve

14. 이병희 14 3D-Rendering  3D models only exist inside computer  When working on a model in 3D application, a rendering operation is needed Rendering high quality images is time consuming Necessary to compromise on quality  Wire frame Used as preview images in modeling program Absence of any surfaces  Hidden surface removal Necessary to determine which surfaces of objects are visible Figure 4.45 wire frame

15. 이병희 15 3D-Rendering  Shading algorithms Interpolate color across each polygon to disguise discontinuities  gouraud shading and phong shading  Paong shading takes account of specular reflection Only deal with each object in isolation Ray tracing  Works by tracing the path of a ray of light Radiosity  Interactions between objects  Attempts to model the complex reflections that occur between surfaces Texture mapping  Adding surface details to 3D models