# Computer Graphics. National Chiao Tung University Chun-Jen Tsai 06/1/2012

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1 Computer Graphics National Chiao Tung University Chun-Jen Tsai 06/1/2012

2 Computer Graphics Computer graphics (CG) is a research topic about authoring and rendering of any visual data, including: Presentation of text Construction of graphics and charts Design of GUI Editing of photographs Creation of animated motion pictures... Today, GC is most often used to refer to 3D graphics 2/21

3 3D Graphics Problem The field of 3D graphics deals with converting 3D shapes into 2D pictures (images) The process involves simulation of the photographic process to convert a digitally encoded scene to a picture Description of a hot-air balloon 3D CG process a digitally encoded scene a 2D picture 3/21

4 3D Graphics Paradigm Three steps in 3D graphics process: modeling, rendering, and displaying display controller CPU rendering using a perspective projection camera model copy the 2D image to the memory cells called frame buffer Memory cells computer 4/21

5 Modeling Problems The modeling step in computer graphics tries to solve the following problems Modeling the shape of a 3D object Modeling the surface characteristics Modeling of the entire scenes 5/21

6 Modeling Shape of an Object (1/2) How do we describe a 3D object? 3D shape can be described by a collection of flat surfaces called planar patches, each of which is a solid polygon The collection of these polygons is called a polygonal mesh n = 12; % resolution of the drawing grid a = 0.2; % the diameter of thesmall tube c = 0.6; % the diameter of the bulb t1 = pi/4 : pi/n : 5*pi/4; % parameter along the tube t2 = 5*pi/4 : pi/n : 9*pi/4; % angle around the tube u = pi/2 : pi/n : 5*pi/2; [X, Z1] = meshgrid(t1,u); [Y, Z2] = meshgrid(t2,u); % The bulb r = sin(y).* cos(y) -(a + 1/2) * ones(size(y)); x2 = c * sin(z2).* r; y2 = -c * cos(z2).* r; z2 = ones(size(y)).* cos(y); surf(x2,y2,z2,y); the precise mathematical description (in Matlab language) of a polygonal mesh a rendered polygonal mesh of quadrangles 6/21

7 Modeling Shape of an Object (2/2) In general, complex objects cannot be described by a simple 3D mathematical function We can use many piecewise smooth functions to describe the contour and shape of a complex object Bezier curves and Bezier surfaces B t) = (1 t) P + 3(1 t) tp + 3(1 t) t P + t P, t [0,1] ( /21

8 Shape Modeling Techniques Geometric modeling e.g., the hot-air balloon model Brute force digitizing of a real 3D object e.g., 3D laser scanning of a real object Procedural modeling (fractals or particle systems) e.g., growing a mountain using a recursive rule (operations) 8/21

9 Modeling Surface Characteristics Surface characteristics of a surface patch is the reaction of the patch to incoming light rays The model has parameters: The frequencies of the incoming light The incidence angle The position on the surface The output of the model: The frequencies and angles of the out-going light at every points on the surface 9/21

10 Texture Maps for Surface Modeling We can encode the color of a surface patch at the vertex only color of other points on the surface are interpolated from the neighboring vertices Another technique is to use a texture map to describe the colors at every points on the surface E F E F A B D C G + A B D C G texture mapping texture map 3D polygonal mesh model 10/21

11 Modeling Entire Scenes A scene can be described by a scene graph that contains the following information Light sources Background descriptions Foreground object descriptions (including their motions) In short, a scene graph describes a virtual world scene lights window background Buzz foreground Woody wall table 11/21

12 Rendering Given a virtual camera, rendering is the process of projecting the objects in a scene onto the projection plane of the camera In computer graphics, the process is achieved using a rendering pipeline, which can be implemented in hardware or software The rendering process is composed of many steps View volume determination Clipping Scan conversion (rasterization) Hidden surface removals Shading 12/21

13 View Volume and Clipping 13/21

14 Scan Conversion A 3D patch is projected onto a digital image result of scan conversion 14/21

15 Hidden Surface Removal If part of a 3D object is covered by other objects, the non-visible part should not be displayed Common techniques for hidden surface removal The painter s algorithm (patch-based technique) The z-buffer method (pixel-based technique) 15/21

16 Shading For each surface patch which is visible in the 2D image, we have to determine the appearance of each pixels as well, this process is called shading Common shading techniques Flat shading Gouraud shading Phong shading 16/21

17 Ray Tracing To render a complete scene with complex objects, a interesting technique is called ray-tracing 17/21

18 Animation (1/2) Computer animation is the technology to use a computer to display successive pictures of a dynamic scene at more than 24 picture per second Each picture is called a frame Today, the standard for smooth animation is to display at least 60 frames per second An animation begins with a story board, which is a sequence of hand-drawing pictures that tells a story: 18/21

19 Animation (2/2) Given a storyboard, artists will refine the pictures in a storyboard into detail frames, called key frames Key frames have much less than 30 frames per second, for animation, we must fill in the gaps between key frames Can we use computers to do this in-betweening for us? 19/21

20 Kinematics and Dynamics Kinematics based on geometry joint 2 what is the motion here? Dynamics based on physics joint 1 If joint 1 rotate 10, and joint 2 rotate 3, what is the motion at the end point? g g Given the mass and center of mass of each object, if we apply some force (torque) on joint 1 & 2, how would the objects move? 20/21

21 Animation Techniques Today Although kinematics and dynamics problems can be solved mathematically using physic theories, today s animation studios don t really do it this way Techniques used in animation studio: By animation artist using drawing software artists draw key frames, computers interpolate the remaining frames By manipulation of skeletal structure models and motion captures of real subject (e.g. human beings) need computational vision technologies 21/21

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