Computer Graphics

Explore the digital differential analyzer (DDA) line drawing algorithm, its slope-based sampling for x or y, and how it plots pixels to render lines, leading to Bresenham's algorithm.

Explore the midpoint circle algorithm for circle drawing in computer graphics. Learn how this algorithm enables accurate circle construction.

We demonstrate the midpoint circle algorithm by plotting circle pixels from a center at 0,0 with radius 10, using the initial decision parameter P0 and eight-way symmetry across quadrants.

Explore the midpoint ellipse algorithm in computer graphics to understand ellipse drawing methods and practical applications.

Explore the midpoint ellipse algorithm by deriving region 1 and region 2 decisions, sampling through the x axis and y axis, using symmetry to plot ellipse boundary pixels.

Learn about filled area primitives in computer graphics and how they define the appearance of shapes.

Explore 2d transformations by translating, rotating, and scaling points on a 2d plane, using tx, ty, theta, cos, sin, and sx, sy.

This lecture explains homogeneous coordinates as xw, yw, 1, enabling all 2d transformations—translation, rotation, and scaling—via matrix multiplication, with examples of translation matrices.

Learn composite transformations in 2d graphics using homogeneous coordinates, showing how two translations add, two rotations sum angles, and two scalings multiply factors, with rotations and scalings about a pivot.

Transforming between coordinate systems requires translating the origin to the target and then rotating the axes to align them, with optional reflection or scaling.

Explore two-dimensional viewing by defining window and viewport, and transform from world coordinates to viewing coordinates through translation, scaling, and window-to-viewport transformation.

Explore 2D clipping concepts, including the clipping window, point clipping, and line clipping, and explain the Cohen-Sutherland algorithm with region codes and intersection-point calculations.

Clip a line against a convex, non-rectangular clipping window using the Cyrus-Beck algorithm with a parametric line, edge normals, and intersection parameters to produce clipping points.

Explore the Sutherland-Hodgman polygon clipping algorithm to clip a polygon against a clipping window by processing each boundary, left, right, upper, and lower, creating intersections and new vertices.

Explore three-dimensional object representation through boundary and space partitioning methods, polygon surfaces, polygon meshes, and quadric surfaces such as spheres and torus.

explores 3d viewing pipeline, converting world coordinates to view coordinates, then to 2d projection coordinates, using modeling, viewing, projection, and workstation transformations; defines view volume, view plane, and viewing parameters.

Explore 3d viewing through projections, contrasting parallel and perspective projections. Learn orthographic and oblique parallel types, projection planes and centers, and the transformation matrix for mapping 3d coordinates to 2d.

Explore how curves represent 3D objects in computer graphics, including implicit, explicit, and parametric curves, and master Bezier curves built from control points to model lines, quadratics, and cubics.

Discover visible surface detection in the 3D viewing pipeline, focusing on back face detection as an object-space pre-processor that removes back faces to speed rendering.

Explore the depth buffer (z-buffer) algorithm for visible surface detection in image space, storing depth values in a depth buffer and intensities in a refresh buffer to reveal closer surfaces.

Apply the scan line visible surface method in image space after back-face removal, using edge, active edge, and polygon tables with depth comparisons to reveal visible surfaces.

Sort surfaces by decreasing depth and scan-convert from farthest to nearest using the depth sorting, or painter's, algorithm. Use image-space and object-space checks with four tests to resolve overlaps.

Explain the bsp tree method for visible surfaces, partitioning space with planes to separate front and back objects as the view changes, building and traversing the tree.

Discover the area subdivision method, an image-space technique that subdivides space into four areas, with backface detection and depth sorting to handle surrounding, overlapping, inside, and outside surfaces.

Explore computer animation fundamentals, including conventional and raster animation, storyboard layout, object and key-frame specifications, in-between frames, and fps roles across entertainment, advertising, and education.

Discover computer animation concepts, from conventional two dimensional animation to raster two dimensional/three dimensional animation, and learn how keyframes, in-between frames, and morphing create motion using color tables and Wavefront.