Principles Of 3D Graphics 3D Three Dimensional Length, Height, Width Contents
• 3D Graphics - Core Ideas • 3D Graphics Modelling & Animation - A Virtual Video • Comparing 2D & 3D Graphics • Layers & Groups • Defining 3D Space • Different Kinds Of Geometry • Geometry For 3D CGI • 3D Space & Co-ordinates • 3D Space & Axes • Coordinate System Review • Lines, Polylines & Polygons • Polygon Components • 3D Objects • Viewpoints • Display Mode • References
3D Graphics - Core Ideas
• 2D representation of 3D objects • Objects only exist in computer memory • No physical form - mathematical formulae
Return to contents 3D Graphics Modelling & Animation - A Virtual Video
• Design objects in a scene. • Assign pre-defined materials or own materials (also known as textures or shaders). • Choose & apply virtual lights & adjust to suit. • Set up virtual cameras to capture & record. • Bring to life (animate) by moving objects & adjusting materials, lights & cameras. • View results by outputting to computer file or a physical medium to play back or show others.
Return to contents Comparing 2D & 3D Graphics
2D • Usually only shows 2 of height, width or length at any one time. • Can imitate 3D but have to redo from scratch to alter view of graphic. Comparing 2D & 3D Graphics
3D • Adds “depth” (inside cyberspace). • Will calculate highlights & shadow information based on objects & lighting. That is, it creates a “painting” based on the colours, textures and lighting the user decides upon. Comparing 2D & 3D Graphics
Drawing tools • 2D & 3D drawing tools are often the same e.g. bezier pen for lines, freehand pencil, circles, arcs, polylines & polygons. • In 3D software these form the basis for creating a 3D object from a 2D shape using techniques such as lofts, sweeps, lathes, extrudes etc.
Return to contents Layers & Groups
Layers • Allow individual editing of elements. • Separate different parts of drawings.
Groups • Ability to combine objects for editing (scaling, moving etc). • Can add, remove & reassign objects to a group.
Both 2D & 3D applications use Layers & Groups.
Return to contents Defining 3D Space
• A mathematically defined cube of cyberspace existing within the computer’s memory. • Like real space 3D space has no real limits, therefore, systems are required to locate objects within the 3D space. • This is typically achieved using a Cartesian coordinate system.
Return to contents Different Kinds Of Geometry
• Descriptive Geometry: aims to represent solid objects in their forms, dimensions & position. Developed by Gaspard Monge (1746-1818). Used in drafting & architecture & employs orthogonal projection. • Projective Geometry: developed during the Renaissance to help painters show figures, building & landscapes in perspective (as we see through our eyes). Solid forms are projected on a picture plane with aid of grids or mechanical devices. • Analytical Geometry: creates a synthesis between geometry & algebra (type of maths) so points, lines, planes & solids can be described with algebraic equations. Developed by Rene Descartes (1596-1650). Makes it possible to represent 3D shapes as numbers in a computer system.
Return to contents Geometry For 3D CGI
• 3D computer graphics uses all three types of geometry. • Allows user to describe complex objects through mathematical methods to create, assemble & render objects to produce a 2D representation that employ the techniques developed by Renaissance era painters & designers.
Return to contents 3D Space & Co-ordinates
• Point: the smallest area “occupied” in 3D space. • Co-ordinates: the definition of that point relative to the centre or “origin” of 0,0,0. 3D software uses these points or co-ordinates to define objects and their position. • Origin: the point at which the three coordinates (X,Y & Z) cross.
Return to contents 3D Space & Axes
• Axis: an imaginary line in cyberspace that defines a direction. • Three standard axes in 3D programs: X,Y & Z. In most 3D design software X = horizontal, Y = vertical, Z = depth. • Plane: Any two axes of a coordinate system eg XZ, XY & YZ.
• Axes can be redefined by the user. Coordinate System Review Coordinate System Review
Return to contents Lines, Polylines & Polygons
• Line: A connection between 2 points • Polyline: Extension of the line to additional points • Polygon: The series of lines that make up the polyline return to the original start point. • A polygon is also known as a closed shape as it has an inside & an outside.
Return to contents Polygon Components
• Vertex: a point where any number of lines come together
• Edge: A boundary of a polygon
• Face: The area enclosed or “inside” the edges of a polygon • Triangle & quad polygons the most common. Can have any number of sides
Return to contents 3D Objects
• Objects in most 3D applications use polygons. • Some use splines (discussed later in course). • Simple objects (few polygons), complex objects (many polygons). • Each vertex in an object defined by a X,Y,Z co-ordinate.
Return to contents Viewpoints
• Viewpoint: position in cyberspace representing location of user. • Default Viewpoint: usually has X axis horizontal, Y axis vertical & Z axis outwards to user. • Viewing Plane: an imaginary flat plane defining the limits of users “sight”. Also know as the “clipping plane”. This is like the limits of one’s peripheral vision. Viewpoints
• In 3D software viewpoint windows are known as “viewports”. • Default viewports typically show orthographic projections, that is, the front, top or side view of objects and also a “perspective” view. • Viewports can be adjusted to suit the user.
Return to contents Display Mode
The display mode of a viewport controls the level of detail of objects. Smooth shaded mode depends on the number of objects and the capability of the users machine, especially the graphics card. • Bounding Box: a box having overall size of an object. • Wireframe: uses lines to show edges of object’s polygons. • Flat Shaded: shows surface & colour in coarse way. • Smooth Shaded: object surface has colour and smoothed surface. • Smooth Textured: begin to looks like a finished image.
Return to contents References
• 3D Graphics & Animation by Mark Giambruno • Principles of 3D Computer Animation by Michael O’Rourke • Getting Started with 3D by Janet Ashford & John Odam • 3ds MAX Help Files
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