1 Preview. Dr. Scott Gordon Computer Science Dept. CSUS. Virtual Cameras, Viewing Transformations: CSc-155 Advanced Computer Graphics

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1 CSc-155 Advanced Computer Graphics 1 Preview Dr. Scott Gordon Computer Science Dept. CSUS Course Description Modeling, viewing, and rendering techniques in 3D computer graphics systems. Topics include: modeling systems and data structures; polygonal and parametric surface representation; 3D transformations and introduction to 3D animation; the synthetic camera paradigm; 3D clipping and projections; hidden surface removal algorithms; techniques for realism such as textures, materials, lighting, shadows, terrain, and atmospheric effects; normal, bump, and height mapping; tessellation; procedural models and fractals. Emphasis on hardware support and shader pipeline programming. 2 3D Modeling: Polygonal Meshes: 3 4 Parametric Surfaces: Virtual Cameras, Viewing Transformations: 5 6

2 Parallel and Perspective Projections: Hidden Surface Removal, Clipping, Culling: 7 8 Color, Lighting, Materials: Shadows: 9 10 Textures: Reflection, Refraction, Transparency: 11 12

3 Terrain, Tessellation: Height mapping, Bump mapping, Normal mapping: Environment Mapping: Fractals: Graphics pipeline, Shader programming: JOGL code Vert shader Tess Control Shader Tess Eval Shader Frag Shader control pts, textures, etc. control pts control pts vertices tesslevels tessellator tesscoords (grid) This is not an easy class: Bleeding edge technology (OpenGL4, JOGL) o Technology changes quickly and often o Most instructional resources are outdated o Books, websites, are rushed, full of typos/errors o Hardware, drivers, always full of bugs o Machines & graphics cards differ in details Debugging shader code is very hard o Not many debugging tools for shader code o No way to print variables o Instructor may not have time to help everyone Expect to put in a lot of time Expect to have to solve many problems yourself! 17 18

4 Prerequisites 19 CSc 133 (Obj-Orient. Comp. Graphics Prog.) which means you must also have: o CSc 15 (Programming Methodology I) o CSc 20 (Programming Methodology II) o CSc 28 (Discrete Structures) o CSc 130 (Algorithms and Data Structures) o CSc 131 (Introduction to Software Engineering) o Math 29 (Pre-calculus Mathematics) Also very helpful: o Math 30 or 26A (Calculus I) o Physics 11A or 5A (Mechanics) Texts and References Required Text: OpenGL SuperBible, 6 th or 7 th Ed., Graham Sellers, et. al., Addison-Wesley 20 JOGL Workbook, Gordon and Clevenger, draft (provided free) Useful References: OpenGL Programming Guide, 8th ed.: The Official Guide to Learning OpenGL, Version 4.3, Shreiner et. al., Addison-Wesley, (also called The Red Book ) Computer Graphics: Theory Into Practice, Jeffrey McConnell, Jones & Bartlett Publishers Interactive Computer Graphics: A Top-Down Approach with WebGL, 7th ed., Edward Angel, Addison-Wesley Programming Experience: Algorithms and Data Structures Linear Lists, Stacks, Queues, Binary Trees, Recursion OOP principles Abstraction, Encapsulation, Inheritance, Polymorphism Design Patterns Java Interface Types Basic GUI Creation Menus, Buttons, Frames, Panels, other widgets Event-Driven Programming Interactive Operations Mouse, Keyboard, and Timer Event Handling Screen-based animation and repaint() operations Math: Matrix Concepts and Operations Matrix addition & multiplication by scalars and vectors Row-major vs. column-major representation; multiplication from the left vs. from the right Multiplication by another matrix: associativity (yes), commutativity (no) Transpose & Inverse Vector Concepts and Operations Definition of a vector; as a single point, or diff. of two points Equivalency after translation Computing Magnitude (length) Multiplication by a scalar value; effect of multiplying by a fractional and/or negative value Definition and computation of Unit vectors Definition and Computation of the Dot Product Graphical Operations: Homogeneous representation of 2D point (x,y) as [ x y 1 ] 23 Matrix Representation for (2D) Translation, Scaling, and Rotation Row vs. Column Forms Proper order of operations Application of Transformation Matrices to Homogeneous Points Concatenation of Transformations Combining multiple transformations into one Use of translation plus rotation about the origin to accomplish arbitrary rotation Coordinate Systems Local, world, device World windows vs. viewports, VTM See CSc 133 Lecture Notes Transformations & Viewing Types & Algorithms: Color Spaces RGB Color Cube & Java Color type Java2D AffineTransform type Points, Lines, and Line Rasterization Cubic Bezier Curves Parametric Representation of lines Control points Blending functions Geometric representation Analytic derivation Recursive drawing algorithm See CSc 133 Lecture Notes Applications of Affine Transforms, Lines & Curves 24

5 Cubic Bezier Curves Review Given 4 control points [P0, P1, P2, P3]: Draw the control mesh (connect the control points) Connect all points of equal parametric value Points with parametric value t are on the curve P 1 P 0112(t) P 12(t) P 2 Analytic Derivation Let P 01 (t) be a point on the line P 0 P 1, and let P 12 (t) be a point on the line P 1 P 2, and let P 23 (t) be a point on the line P 2 P 3 (see previous diagram). Then and and P 01 (t) = t P 1 + (1-t) P 0 [1] P 12 (t) = t P 2 + (1-t) P 1 [2] P 23 (t) = t P 3 + (1-t) P 2 [3] P 01(t) P(t) P 1223(t) Likewise, let P 0112 (t) be a point on the line P 01 (t) P 12 (t), and P 1223 (t) be a point on the line P 12 (t) P 23 (t). Then, P 0112 (t) = t P 12 (t) + (1-t) P 01 (t) [4] P 0 P 23(t) Following this same procedure, substituting, and then solving for P(t) gives P(t)= (1-t) 3 P 0 + (3t 3-6t 2 +3t) P 1 + (-3t 3 +3t 2 ) P 2 + (t 3 ) P 3 25 P 3 Thus we say that the curve defined by [P 0, P 1, P 2, P 3 ] is the set of all points P(t) such that P(t) = (P i B i (t)) 26 Control Mesh Subdivision Splitting a control mesh [Q] at t=1/2 produces two meshes [R] and [S] [R] and [S] each define curves which are identical to the left and right halves of the original curve [Q] Q1 Q2 Subdivision Drawing Algorithm /** Draws the (cubic) Bezier curve represented by the (1x4) input Control Point * Vector by recursively subdividing the Control Point Vector until the control * points are within some tolerance of being colinear, at which time the Control * Points are deemed "close enough" to the curve for the 1st and last control * points to be used as the ends of a line segment representing a short piece of * the actual Bezier curve. */ (R2) (R3) (S0) (S1) void drawbeziercurve (ControlPointVector, Level) { if ( straightenough (ControlPointVector) OR (Level > MAXLEVEL) ) { (R1) (S2) else { draw line from 1st control point to last control point ; subdividecurve (ControlPointVector, LeftSubVector, RightSubVector) ; (R0) Q0 R0 = Q0 ; R1 = (Q0 + Q1) / 2 ; R2 =( (R1) / 2) + ( (Q1+Q2) / 4); R3 = (R2+S1) / 2; (S3) Q3 drawbeziercurve (LeftSubVector,Level+1) ; drawbeziercurve (RightSubVector,Level+1) ; Subdivision Algorithm (cont.) /** Splits the input control point vector Q into two control point vectors R and S such that * R and S define two Bezier curve segments that together exactly match the Bezier curve * defined by Q. */ void subdividecurve (ControlPointVector Q, R, S) { R(0) = Q(0) ; R(1) = (Q(0)+Q(1)) / 2.0 ; R(2) = (R(1)/2.0) + (Q(1)+Q(2))/4.0 ; S(3) = Q(3) ; S(2) = (Q(2)+Q(3)) / 2.0 ; S(1) = (Q(1)+Q(2))/4.0 + S(2)/2.0 ; R(3) = (R(2)+S(1)) / 2.0 ; S(0) = R(3) ; /** Determines whether the four points in the input array are within some tolerance * "epsilon" of being colinear; returns true if so, otherwise returns false. */ boolean straightenough (ControlPointVector q) { d1 = lengthof(q0,q1) + lengthof(q1,q2) + lengthof(q2,q3); d2 = lengthof(q0,q3) ; if ( abs(d1-d2) < EPSILON ) //typical Epsilon (error tolerance) e.g return true ; else return false ; 29 This Week Make sure you have Java 1.8 If you are using your own machine: 30 o make sure it supports OpenGL 4.3 or higher (use verification tool) o install JOGL (handout on course website) o install graphicslib3d (download from course website) Do the assigned readings on the course schedule.