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Introduction to 3D Computer Graphics and Virtual Reality McConnell text.
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Transcript of Introduction to 3D Computer Graphics and Virtual Reality McConnell text.
![Page 1: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/1.jpg)
Introduction to 3D Computer Graphics and Virtual Reality
McConnell text
![Page 2: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/2.jpg)
Vectors
• Vectors have direction and magnitude – generally given in terms of three coordinates and hence the representation is an arrow from the origin to that point
• Vectors are important for viewpoint, orientation, scaling, rotating and other transformations
(3,1,1)
![Page 3: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/3.jpg)
Vectors (con’t)
• Length: ||v||=
• Addition, scalar multiplication
• Dot product:
• Cross-product: vector that is perpendicular to both
2 2 2x y z
|| || || || cosv w v w
Courtesy Wikipedia for symbols
![Page 4: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/4.jpg)
Camera
• Point of view of a camera; viewpoint
• Clipping window is the part of the scene that is visible
• View direction
• What is up?
![Page 5: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/5.jpg)
Coordinate Systems• 3D coordinate system – right or left handed (curl
fingers from pos X-axis to pos Y-axis: thumb points pos Z)– Virtools is left-handed, Processing is left-handed, but the y axes (and hence the z axes) point in opposite directions
X
Virtools Processing
Z Y
• 2D screen coordinate system:
X
Z
Y
X
Y
![Page 6: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/6.jpg)
Coordinate System: 3D Environments
• Most 3D environments have at least two coordinate systems: a world coordinate system and a local coordinate system for each object (sometimes parts of objects)
• The world coordinate system does not change
• The local coordinate system is generally located in the “middle” or in a corner of the object and is set in the 3D modeling program.
![Page 7: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/7.jpg)
Coordinate Systems (con’t)
• Clipping window is the visible area of the 3D scene (it is 2D)- window through which you look
• Viewport is where on the screen (also 2D) the visible scene appears; uses the coordinate system of the screen
• The viewport and the clipping window may be different sizes, in which case there is stretching or squishing
• Aspect ratio= width/height- easier if both clipping window and viewport have same
![Page 8: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/8.jpg)
Interplay of 2D and 3D systems
• There are often 2D objects (buttons, interfaces, screen text) – these are in the 2D system
• 3D objects must actually be rendered on the screen so they ultimately end up with 2D coordinates
• This projection onto the screen must take into account the z-position of objects, as well as perspective
![Page 9: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/9.jpg)
Orientation
• Objects in a 3D world have spatial location (position) and orientation
• Orientation is given in many different forms: pitch, roll, yaw or Euler angles (around each axis); quaternions
• In Processing can rotate in 2D or in 3D around the axes
• In the Virtools setup Euler angles are used for orientation
![Page 10: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/10.jpg)
Object Representation• 3D objects are represented with meshes; points
that are joined together in convex, planar polygons (faces); typically these polygons are triangles because then there is assurance that they will be planar
• The set of points forms the mesh• Each face of the mesh may have a material
associated with it; these materials can be textures and/or colors
• Details (and realism) increase with the numbers of polygons
![Page 11: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/11.jpg)
Point Representation
• These representations allow for algorithms for calculation of intersections, collisions, positioning
• Also have algorithms to find which objects are in front, partial view, occlusion
• For speed, objects can be surrounded by a bounding box – allows quick calculation of intersections
![Page 12: Introduction to 3D Computer Graphics and Virtual Reality McConnell text.](https://reader035.fdocuments.in/reader035/viewer/2022071717/56649e175503460f94b030ae/html5/thumbnails/12.jpg)
Graphics Pipeline
• Model the individual objects (color, transformations, realism, where located) and together they constitute a scene
• Render the scene (lights, shading, camera, etc.) in an image
• Display the image as output
• If in a virtual environment have real-time, interaction and navigation