Shop Solver

Point Tool

Command path:  Quick->Point
The purpose of this tool is to define points and to perform simple operations upon them.

Overview

The tool's window is divided into two sections.  The upper section is for defining a point by its X, Y and Z values.  The lower section contains operations that may be performed on the point.

To define a point enter its X, Y and Z values in the designated entry fields.  To save the point definition to memory enter the point's name in the Name  field and click Save.  A definition may be recalled later by selecting the name from the Name  field's drop down list.  Saving a definition in memory is optional and is not required for performing operations upon the point.  All definitions saved in memory are lost when Shop Solver is closed.  See the File commands for saving and loading definitions to and from a file.

Operations upon a point definition only affect the values in the X, Y and Z definition fields, when applicable.  Point definitions saved in memory are not affected.

All numeric entry fields in Shop Solver can evaluate and solve mathematical expressions.  You may enter expressions using the common arithmetic operators +, -, *, /, (, ), %, and ^.  In addition 30+ functions are supported such as trigonometric functions, common math functions (square and cube roots, absolute values, min/max, etc.) and common shop functions such as surface feet per minute (SFM) to RPM, inch to millimeter, and others.  Expressions are evaluated when an entry field loses the focus by tabbing to or clicking on something else.  For a full description of this feature click here.


Image Point



Point Operations

Rotate
The rotate operation is 2D and only in the XY plane.  To rotate the point defined in the Point definition section around the origin (i.e. around X0, Y0) enter the angle of rotation in the entry field immediately to the right of the Rotate  button and then click Rotate.  Rotation angles must be specified in degrees.  The result of the rotation replaces the X and Y values in the Point definition section.  The Z value is not affected.

To rotate the point definition around another point other than the origin, select the point of rotation from the drop down list or type the name of the point into the drop down list's entry field.  Enter the angle of rotation in the entry field immediately to the right of the Rotate  button and then click Rotate.  The result of the rotation replaces the X and Y values in the Point definition section.  The Z value is not affected.

Click here to learn how to rotate a point simultaneously around all 3 axes.

Example to rotate the point X1.0 Y0 45 degrees counter-clockwise twice:
1) Enter 1 in the X field and 0 in the Y field.
2) Enter 45 in the rotation field.
3) Click the Rotate  button.  The X and Y entry fields now show 0.7071 respectively.
4) Click the Rotate  button again to rotate X0.7071 Y0.7071 45 degrees.  The X and Y entry fields now show X0 Y1.0.

Click here to see how positive and negative angles of rotation are determined.

Figure 9 shows another example in which a partial bolt circle is depicted:



The bolt circle is centered on P1 which is located at X9.0 Y7.0.  The first hole is at 15 degrees and the next 3 are 30 degrees apart.  To determine the hole locations:
1) Define and save point P1.
2) Enter 9+5 in the X entry field and 7 in the Y entry field.  This defines a point that would be the location of a hole at 0 degrees on the bolt circle, i.e. at X14.0 Y7.0.
3) Enter 15 in the rotation field and select P1 in the point of rotation drop down list.
4) Click the Rotate  button.  The X and Y entry fields show the location of the first hole: X13.8296 Y8.2941
5) Enter 30 in the rotation field and click the Rotate  button.  The X and Y entry fields show the location of the second hole: X12.5355 Y10.5355
6) Click the Rotate  button for the third hole: X10.2941 Y11.8296
7) Click the Rotate  button for the fourth hole: X7.7059 Y11.8296

Scale
The scale operation multiplies the X, Y and Z values of the point definition by the specified scaling factor.  Enter the scaling factor in the entry field to the right of the Scale  button and then click the button.    The result of the scale operation replaces the X, Y and Z values in the Point definition section.

Mirror Line
The mirror operation mirrors the point definition's X and Y values about a specified mirror line.  Mirroring is a 2D operation and is only in the XY plane.  If the mirror line does not lie in the XY plane then it is projected onto the XY plane and mirroring is performed about the projection.  As a result the source point and the mirrored point are equidistant from the line.  A line drawn through the source and mirrored points is perpendicular to the specified mirror line.

To mirror a point definition:
1) Enter the point's X and Y values in the Point definition section or select a point from the Name  drop down field.  The Z value is not used or affected.
2) Select the mirror line from the Mirror Line  drop down field.  The result of the operation replaces the X and Y values in the Point definition section.

An example is shown in Figure 10:


Figure 10 shows the source point P1 at X-4.0 Y6.0 and the mirror line L1 (defined as passing through X8.014 Y8.2167 at angle 50.1943).  The mirror operation results in point P2 at X8.0 Y-4.0.  Both points are 7.8102 units from L1 and a line extending through P1 and P2 is perpendicular to L1.

Dx to Point
This operation calculates the distance between the point definition and another point.  To find the distance between 2 points:
1) Enter the first point's X, Y and Z values in the Point definition section or select a point from the Name  drop down field.
2) Select the second point from the Dx to Point  drop down field.  The distance between the points is shown to the right of the drop down field.

Dx to Line
This operation calculates the shortest distance between the point definition and a specified line.  To find the distance from a point to a line:
1) Enter the X, Y and Z values of the point in the Point definition section or select a point from the Name  drop down field.
2) Select a line from the Dx to Line  drop down field.  The shortest distance between the point and the line is shown to the right of the drop down field.

Dx to Circle
This operation calculates the shortest distance between the point definition and a specified circle.  To find the distance from a point to a circle:
1) Enter the X, Y and Z values of the point in the Point definition section or select a point from the Name  drop down field.
2) Select a circle from the Dx to Circle  drop down field.  (Note:  Only circles in the same plane as the point definition and that lie in a plane parallel to the XY plane appear in the drop down field.)  The shortest distance between the point and the circle is shown to the right of the drop down field.

Dx to Plane
This operation calculates the shortest distance between the point definition and a specified plane.  To find the distance from a point to a plane:
1) Enter the X, Y and Z values of the point in the Point definition section or select a point from the Name  drop down field.
2) Select a plane from the Dx to Plane  drop down field.  The shortest distance between the point and the plane is shown to the right of the drop down field.

Click here to learn how to define a plane.

Incremental Dx
This operation calculates the signed X, Y and Z distances from a specified point to the point definition.  This operation is akin to calculating the I, J and K incremental distances when programming a G-code arc.  To find the incremental distances from a specified point to the point definition:
1) Enter the X, Y and Z values of a point in the Point definition section or select a point from the Name  drop down field.  In the G-code arc analogy this point would represent the center point of the arc.
2) Select a point from the Incremental Dx  drop down field.  In the G-code arc analogy this point would represent the start point of the arc.  The incremental X, Y and Z distances replace the values in the Point definition section.

Copy Button
The Copy button copies the X, Y and Z point definition values to the clipboard.

Reset Button
The Reset button clears all of the fields on the tool.