Coordinate Systems 6.3

Basic Terms and Concepts

• Coordinate systems define points or other elements in space
• Each numeric value (coordinate) associated with a dimension
• Each linear dimension is represented by an axis
• Relationship of dimensions define coordinate system
• Each dimension may have its own unit of measure
• A set of coordinates with values of zero is the origin
• Visual representations of coordinate systems are called graphs

Types Of Coordinate Systems

• Cartesian
• Mutually perpendicular axes
• Typically two or three dimensions
• Axes define dimensions
• Quadrants are area between axes
• Polar
• Defined by a linear axis and one angular dimension
• Distance from the origin defines measure on linear axis
• Angular dimension must be defined by a reference angle and cw or ccw rotation

Application/Conventions

• Labeling and orientation
• Horizontal axis usually labeled X
• Vertical axis usually labeled Y
• Third axis (if any) usually labeled Z
• Numbering
• Positive numbers are usually up, to the right, or ccw
• Negative numbers are usually down, to the left, or cw
• Cartesian coordinates are stated in the order (X, Y, Z)
• Polar coordinates are stated in the order (Distance, Angle)
• Absolute coordinates
• Defined relative to the coordinate system origin
• Relative coordinates
• Defined relative to another location

Representing time 20.3.2

• Points in time
• A representation (picture/snapshot) of current state
• A position along a graph axis
• Discrete changes in time
• A series of pictures/images
• Arrows or step numbers on a diagram
• Multiple positions along a graph axis
• Continuous changes in time
• Animation
• Continuous element on a graph or diagram
• lines
• arrows
• ribbons

Projection Techniques

Orthographic Projection 8.2

• Glass box metaphor
• Six mutually perpendicular planes of projection
• Unfolding the box and the lines of intersection
• Relationship to planes of projection to ports in 3-D modeling software
• Separate views of the same object
• Choice of views
• Capturing of 2-D views of 3-D objects

Pictorial Projection

• Capture all three dimensions in one view
• Type of projection
• Axonometric 9.1
• Isometric
• Dimetric
• Trimetric
• Oblique 9.5
• Perspective 10.1-10.4
• Convergence of parallel edges

Guidelines for Applying Projection Method

• Arrangement of orthographic views
• Parallel vs. Perspective projection
• Dimensional accuracy of views
• Visual realism

Sketching

Uses 4.1, 4.4

• Representing objects
• Ideation
• Documentation
• Representing ideas
• Diagrams
• Flow Charts
• Visualizations

Techniques

• Lines 4.2
• Straight
• Curved
• Proportioning 4.3
• Construction lines
• Layout
• Darkening
• Pictorials 4.5.1-4.5.4
• Multiviews 4.5.5

Biology Modeling Example

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