Chapter 4 Digital Multimedia, 2nd edition Vector Graphics

4 Compact Scalable Resolution-independent Hence attractive for networked multimedia Vector Graphics 86

4 Vector Graphics Not widely used on WWW until the arrival of Flash SVG is an open standard supported by many web browsers, but few people use this format. SVG format: Example: Flash is proprietary (well, for now…)

4 Proprietary vs. Open What is the difference between standard open file formats and proprietary formats?

4 Any point in the plane can be identified by its horizontal and vertical distance from the origin P = (x, y) Coordinates 87

4 Specify a displacement by movements in x and y directions (not Euclidean distance) 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 Vectors 88

4 Represent lines, curves, shapes,... by parameters of their defining equations e.g. line y = mx + c, store m and c (or endpoints) Compute pixels which must be set in order to draw the line etc Rendering 88–89

4 Rendering In general, rendering will exhibit 'jaggies' Pixels' coordinates are integers, equations use real numbers

4 Rendering is sampling & reconstruction Abstract continuous line must be approximated by discrete pixels of finite size Jaggies are instance of phenomenon of aliasing Aliasing 89–91

4 Anti-aliasing Mitigate effect by colouring pixels in shades of grey (for a black line), brightness varies according to extent of intersection with an idealized 1 pixel wide line

4 Anti-aliasing

4 Drawing programs and vector graphics languages provide basic repertoire of shapes that can easily be represented mathematically Rectangles and squares (may have rounded corners) Ellipses and circles Straight lines, polylines and polygons Smooth (Bézier) curves Shapes 91–92

4 Smooth curves completely specified by four control points 2 endpoints (P 1, P 4 ) 2 direction points (P 2, P 3 ) Sweep of the curve is determined by length and direction of lines from endpoints to direction points Bézier Curves 92–94

4 Bézier curves can be easily combined to make elaborate smooth paths Closed path joins up on itself, open path doesn't Paths 94–96

4 Paths Good “Drawing” programs let you create smooth natural curves. Let me show you an example

4 Apply stroke to make path visible (like tracing with ink) Specify width and colour etc Apply fill to closed path or shape (like colouring it in) Specify colour or a gradient or pattern Gradients may be linear or radial; Illustrator also supports mesh gradients Stroke & Fill 96–99

4 Manipulate vector objects in certain ways by changing stored values that describe them Translation (linear movement) Scaling Reflection Rotation Shearing (skewing) Perform transformations with direct manipulation (tools) or numerically (dialogue) Transformations 101–102

4 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, etc 3-D Vector Graphics 103–104

4 3-D Vector Graphics Practically complicated and difficult Requires 3-D visualization skills Complex tools are hard to master Considerable processing power is needed

4 Start with mathematical model of objects in 3-D space, need a 2-D picture, usually in perspective Need to define viewpoint (camera position) Must consider lighting Can have different light sources – spots, diffuse,... Surface characteristics of object (texture, shininess, etc) determine how it appears under different lighting conditions Need a model based on physics of light 3-D Rendering 105

4 Build 3-D models out of a few primitive objects – cube, cylinder, sphere, pyramid,... Apply distortions such as squashing or stretching Combine objects using spatial equivalents of set operations Union, intersection, difference Constructive Solid Geometry 106

4 Use object's boundary surface to define it use of outline to define 2-D shape Construct surface as mesh of flat polygons Use triangles for fast rendering (games) Can generalize Bézier curves to 3-D surfaces Generate objects by sweeping 2-D cross section along a path Extrusion and lathing Free Form Modelling 106–108

4 Define an object by giving algorithm for constructing it Fractals Exhibit same structure at all levels of detail Model landscape features, clouds etc Metaballs Coalescing fields around spheres Model soft objects Particle systems Procedural Modelling 108–111

4 Wire frame Simple mathematical projection of 3-D model Useful for previews Hidden surface removal Non-trivial, but well understood Can colour surfaces arbitrarily, sufficient for removing visual ambiguity of wire frame 3-D Rendering 111–112

4 Interpolate colour across each polygon to disguise discontinuities Gouraud and Phong shading Phong shading takes account of specular reflection Take account of interaction between objects Ray tracing and radiosity Shading Algorithms 113–114