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Published byMolly Harrington Modified about 1 year ago

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3D REPRESENTATION 2D REPRESENTATION SHARED GRAPHICS SKILLS CAMERAS AND CLIPPING PLANES Principles of Graphical Representation using Computer Graphics Software

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“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

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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.

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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 the same, with the Z axis being a value other than zero in 3D.

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

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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.

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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

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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

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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

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

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

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

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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.

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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

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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

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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

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Clipping Planes

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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

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