Principles of Graphical Representation using Computer Graphics Software

1. Principles of Graphical Representation using Computer Graphics Software 3D Representation 2D Representation Shared Graphics Skills Cameras and Clipping Planes

2. “Workspace” or “Scene” • An Imaginary Cubic Boundary • Cartesian Coordinate System • X, Y, Z Axes • 0,0,0 is the Origin • Z up or Y up

3. Geometry Building Blocks • Point – also referred to as a vertex – the base geometric element in a computer graphics modeling package • Line – also referred to as Splines in 2D or Edges in 3D – at least 2 vertices, but can contain multiple vertices to become a contiguous string of segments • Closed Spline or Polyline • Open Spline • Plane – in Polygonal modeling / geometry consists of triangular Faces and N-Sided Polygons – contains at least 3 Edges • The manipulation and plotting of the spatial relationships of these components require a coordinate system.

4. Cartesian Coordinate System • Points are always plotted in the order of X, Y, Z • From the Origin, each plotted point is measured negative or positive • Quadrants • Right-Hand Rule • 2D and 3D is thesame, with the Z axis being a value other than zero in 3D.

5. Polar Coordinate System • Polar Coordinates – Angle then Distance – Positive Counts Counter-Clockwise from Zero

6. Absolute vs. Relative Coordinates • Absolute Coordinate Input – Each point is always plotted relative to the Origin. • Relative Coordinate Input – Each point is plotted relative to the last input.

7. Relative Coordinates – Object Coordinate System • Using Object Coordinate System (Relative Coordinates) each object has its own origin • Transformations and manipulations in an Object Coordinate System are relative to the object rather than the world origin. • This makes it easier to transform and manipulate the objects

8. Graphical Representation • The vast majority is 2D representation of 3D objects • Technical Documentation – Construction Documents, basic communication with peers • 3D conception –> 2D representation –> 3D realization • Computer Models can be “photographed” – images and line drawings can be generated much faster than can be drawn • Extraction Methodology – design in 3D, extract 2D

9. Orthographic Projection • A means of representing a three-dimensional (3D) object in two dimensions (2D) • A perspective projection with a hypothetical viewpoint—e.g., one where the camera lies an infinite distance away from the object and has an infinite focal length, or "zoom". (parallel projection) • Multi-view Orthographic Projection • Axonometric Orthographic Projection Non-Orthographic (Perspective) Orthographic

10. Multi-View Orthographic • Each projection plane is parallel to one of the coordinate axes of the object resulting in visual distortion / abstraction

11. Architectural Plan • Also called plan view. a drawing made to scale to represent the top view or a horizontal section of a structure

12. Architectural Section • A representation of an object as it would appear if cut by a plane, showing its internal structure.

13. Architectural Elevation • A drawing or design that represents an object or structure as being projected geometrically on a vertical plane parallel to one of its sides.

14. Axonometric • Axonometric • A skewed Orthographic Projection so that multiple sides are visible at once • a three-dimensional object is represented by a drawing having all axes drawn to exact scale, resulting in the optical distortion of diagonals and curves • Trimetric – arbitrary foreshortening • Isometric

15. Isometric • Isometric • a three-dimensional object is represented by a drawing having the horizontal edges of the object drawn usually at a 30° angle and all verticals projected perpendicularly from a horizontal base, all lines being drawn to scale

16. Clipping Planes • Uses Orthographic Cameras – Relatively Universal • Extracts from solids or surfaces alike • Uses two planes perpendicular to the focal length of the camera – Near Clipping Plane and Far Clipping Plane • Only displays graphical information between the near clip and the far clipping plane

17. Clipping Planes

18. Plotting to File with Clipping Planes • The clipping plane method can be used in conjunction with the plot to file method. Plotting to file allows three important options in a single method – • Allows rendering – allows the use of hidden line projection to “hide” lines that should be obscured with planes in 3D space. • Flattens the drawing – gets rid of the Z dimension and flattens the 3D model to a 2D vector drawing • Separates the line drawings – Drawings can be edited in respect to themselves without adversely altering the model