Understanding 3D Coordinate Systems: Types, Rules, and Points, Slides of Computer Graphics

Download Understanding 3D Coordinate Systems: Types, Rules, and Points and more Slides Computer Graphics in PDF only on Docsity! Computer Graphics Lecture 16 Docsity.com 3-D Concepts Docsity.com Casting the shadow of a 3D image Docsity.com Coordinate Systems Coordinate systems are the measured frames of reference within which geometry is defined, manipulated and viewed. Docsity.com Coordinate Systems In this system, a point serves as the origin (reference point), and three lines (axes) that pass through this point and are orthogonal to each other (at right angles – 90 degrees). Docsity.com 1-D Coordinate System Direction and magnitude along a single axis, with reference to origin Locations are defined by a single coordinate Docsity.com Can define points, segments, lines, rays Can have multiple origins (frames of reference) and transform coordinates among them Docsity.com 1-D Coordinate System Docsity.com 2-D Coordinate System Docsity.com 3-D Coordinate System It is 3D Cartesian coordinate system Direction and magnitude along three axes, with reference to an origin Locations are defined by x, y, z triples Docsity.com Can define cubes, cones, spheres, etc., (volumes in space) in addition to all one- and two-dimensional entities Can have multiple origins (frames of reference) and transform coordinates among them Docsity.com Most world and object axes tend to be right handed Left handed axes often are used for cameras Docsity.com Left handed versus Right Handed Rules Docsity.com “Right Hand Rule” for rotations: grasp axis with right hand with thumb oriented in positive direction, fingers will then curl in direction of positive rotation for that axis. Docsity.com Right hand rule -Z +Z +X +Y East North West Origin South -X -Y Docsity.com Defining Left hand rules Left handed Cartesian coordinate system describes the relationship of the X, Y and Z in the following manner: Docsity.com –X is positive to the right of the origin, and negative to the left. –Y is positive above the origin, and negative below it. –Z is positive beyond the origin, and negative behind it. Docsity.com Thus the origin of the Coordinate system is located at point (0,0,0) While five units to the right of that position might be located at point (5,0,0). Docsity.com Y-up versus Z-up z-up typically used by designers y-up typically used by animators Docsity.com Y-up versus Z-up orientation by profession supposedly is derived from past work habits often handled differently when moving from application to application Docsity.com Locations can be relative to any of these coordinate systems Locations can be translated or "transformed" from one coordinate system to the other. Docsity.com |. local (obyect) * axes 7 gh ob a\ (wor \d) exes Global and Local Coordinate systems Multiple Frames of Reference in a 3-D Scene Multiple Coordinate Systems within any 3-D scene Docsity.com Defining points in C language structure Define a point in 3D How far East, Up, and North it is from origin. The center of your computer screen? Docsity.com If it would be at a point such as “1.5 feet east, 4.0 feet up, 7.2 feet north.” A data structure is required to hold these values. Docsity.com POINT3D structure typedef struct _POINT3D{ float x; float y; float z; } POINT3D; POINT3D screenCenter = {1.5, 4.0, 7.2}; Docsity.com Defining Geometry in 3-D Here are some definitions of the technical terms that will be used in 3D. Docsity.com Modeling Modeling is the process of describing an object or scene so that we can construct an image of it Docsity.com Points •Points are the three- dimensional locations (or coordinate triples) Docsity.com BYere-) Wee) At] Polygons •sequences of “correctly” co-planar points; or an initial point and a sequence of vectors Docsity.com Polygons Docsity.com Polygon strips or meshes Meshes provide a more economical description than multiple individual polygons Docsity.com 100 individual triangles, each having 3 vertices, would require 100 x 3 or 300 vertex definitions to be stored Docsity.com In contrast, triangle strips require n + 2 vertex definitions for n number of triangles in the strip. Hence, a 100 triangles strip requires only 102 unique vertex definitions. Docsity.com 3D shapes are represented by polygonal meshes that define or approximate geometric surfaces. Docsity.com With curved surfaces, the accuracy of the approximation is directly proportional to the number of polygons used in the representation. Docsity.com More polygons (when well used) yield a better approximation. But more polygons also exact greater computational overhead, thereby degrading interactive performance, increasing render times, etc. Docsity.com Sampling The process of selecting a representative but finite number of values along a continuous function sufficient to render a reasonable approximation of the function for the task at hand. Docsity.com Level of Detail (LOD) To improve rendering efficiency when dynamically viewing a scene, more or less detailed versions of a model may be swapped in and out of the scene database depending on the importance (usually determined by image size) of the object in the current view. Docsity.com Surface normal A vector perpendicular to a surface and “outward” facing Surface normal are used to determine visibility and also in the calculation of shading values Docsity.com