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Using three-dimensional coordinates

May 20, 2011

Specifying coordinates in three dimensional space is similar to working in two dimensions, except that you also use the z axis to locate coordinates. Three dimensional coordinates are represented in the format x,y,z (2,3,6).


Using the right hand rule

       To visualize how ZWCAD works with three dimensional space, use a technique known as the right hand rule. Hold up your right hand in a loose fist with your palm facing you. Extend your thumb in the direction of the positive x axis and your index finger upward in the direction of the positive y axis. Then extend your middle finger straight toward you in the direction of the z axis. These three fingers are now pointing in the positive x, y, and z directions, respectively.

       You can also use the right hand rule to determine the positive rotation direction. Point your thumb in the positive direction of the axis about which you want to rotate, and then curl the rest of your fingers toward your palm. These fingers are curling in the positive rotation direction.

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The right hand rule helps you determine the positive direction of the x, y, and z axes and the positive rotation direction.


Entering x,y,z coordinates

        When working in three dimensions, you can specify x,y,z coordinates as absolute distances in relation to the origin (the (0,0,0) coordinate point at which the three axes intersect) or as relative coordinates based on the last point selected. For example, to specify the coordinate (3,4,2), just specify a point 3 units along the positive x axis, 4 units along the positive y axis, and 2 units along the positive z axis.


Entering spherical coordinates

        When working in three dimensional space, you can use spherical coordinates to specify a three dimensional point by entering its distance from either the origin (absolute distance) or the last point (relative distance), along with its angle in the xy plane and its angle up from the xy plane. In spherical format, you separate each angle with the open angle bracket (<).You can enter the coordinate values using the following format: X < [angle from X axis] < [angle from XY plane]

      Thus, to draw a line from the origin to a point 10.2500 drawing units away, at an angle of 45 degrees from the x axis and 35 degrees from the xy plane, start the Line command, and then respond to the prompts as follows:

Start of line: 0,0,0

Angle/Length/<End point>: 10.2500<45<35

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When you draw a line from a start point (A) to an endpoint (B) using spherical coordinates, you specify its length (C, in this case 10.2500 units), the angle in the xy plane (D, in this case 45 degrees), and the angle from the xy plane (E, in this case 35 degrees).


Entering cylindrical coordinates

      When working in three dimensional space, you can also use cylindrical coordinates to specify a three dimensional point. You specify a point by entering its distance from either the origin (absolute distance) or the last point (relative distance), its angle in the xy plane, and its zcoordinate value.

      In cylindrical format, you separate the distance and angle with the open angle bracket (<) and separate the angle and z value with a comma. You can enter the coordinate values using the following format X < [angle from X axis],Z For example, to draw a line from the last point to a point 7.4750 units away, at an angle of 27 degrees from the x axis in the xy plane and 3 units up in the z direction, start the Line command, and then respond to the prompts as follows:

Start of line: (select point A)

Angle/Length/<End point>: @7.4750<27,3

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When you draw a line from a start point (A) to an endpoint (B) using cylindrical coordinates, you specify its length (C, in this case 7.4750), the angle in the xy plane (D, in this case 27 degrees), and the distance in the z direction (E, in this case 3 units).

Commands Reference

BLIPMODE: Controls the display of marker blips

ID: Displays the coordinate of a location

LIST: Displays database information for selected objects

GRID: Displays a dot grid in the current viewport

SNAP: Restricts cursor movement to specified intervals

TABLET: Calibrates, configures, and turns on and off an attached digitizing tablet

UCS: Manages user coordinate systems

UCSICON: Manages defined user coordinate systems

UNITS: Controls coordinate and angle display formats and precision

System Variables Reference

BLIPMODE: Controls whether marker blips are visible

COORDS: Controls when coordinates are updated on the status line

LASTPOINT: Stores the last point entered, expressed as a UCS coordinate for the current space; referenced by the at symbol (@) during keyboard entry

ELEVATION: Stores the current elevation relative to the current UCS for the current viewport in the current space

TABMODE: Controls the use of the tablet 

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