Shop Solver

Line/Line Tool

Command path:  Quick->Line/Line
The purpose of this tool is to determine the intersection point of 2 lines, if any.

Quick Start

This tool is two-dimensional (2D).  Both lines must lie in the same plane and the plane must be parallel with the XY plane.  Refer to the Line definitions for information about three-dimensional lines and operations on them.

To find the intersection point of two lines:
1)  In the box labeled "Line 1", select whether the line will be defined as passing through a known point at an angle (Point/Angle) or passing through two known points (Point/Point).
2)  For "Point/Angle" enter the X and Y values of the point and the angle in degrees.  For "Point/Point" enter the X and Y values for both points.
3)  Repeat steps 1 and 2 for Line 2.
4)  Click the Calculate  button.  If the button is disabled then tab to or click on another field (such as the Offset  field).  The point of intersection is shown in the fields above the button.

For information about the Offset  fields click here.


Overview

The application window is divided into three sections.  The upper two sections are for defining the two lines.  The lower section displays the result of the intersection calculation.  The buttons in the lower section are described below.


Image LineLine1



Referring to image LineLine1 above, a line may be defined as:
1) passing through a point and at an angle (in degrees) with the positive X-axis, or
2) passing through two points.

The radio buttons "Point/Angle" and "Point/Point" are used to specify which type of line definition is desired.  Figure 1 below shows line L1 passing through X3.0, Y2.0 and at an angle of +30 degrees with the positive X-axis.  Line L2 passes through the two points X-3.0, Y4.0 and X-7.0, Y13.0.  Both lines are shown entered into the line definition sections in image LineLine1 above.






Figure 2 shows how positive and negative angles are determined.



Figure 3 shows another example of two lines, L1 and L2, that intersect:



Image LineLine2



Image LineLine2 shows the coordinates of the points and angles of lines L1 and L2 from Figure 3.  The angle shown for Line 2 was calculated by Shop Solver after the coordinates of the two points were entered.  The angle field is disabled and shown with a gray background because it is only for reference in a Point/Point definition.

The bottom section of Image LineLine2 shows the point of intersection of lines L1 and L2 after the Calculate  button was clicked.  The Copy  button, when clicked, copies the X and Y values of the point of intersection to the clipboard.  The Reset  button clears all fields in the window.

The Name  fields are used in conjunction with the Save  buttons.  When a name is specified the Save  button stores the line definition in memory.  The 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 calculating intersections.  If not saved to a file, all definitions saved in memory are lost when Shop Solver is closed.  See the File command for saving and loading definitions to and from a file.

A Point definition may be created by right-clicking with the mouse on any of the X fields.  A pop-up menu will appear with a Create Point  command.  The command will take you to the point definition tool and the X, Y, and Z (Z when applicable) values will be automatically entered into the proper fields.  For more about point definitions click here.

If any points have been saved in memory then their X and Y values may be automatically pasted into the line definition fields.  Right-click on any X field in the line definitions and a pop-up menu will appear with the names of all points currently saved in memory.  Select a point to paste its X and Y values into the fields.

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.

Line Offsets

The usage of the Offset  fields is depicted in Figure 4.  The outline of a simple part is shown in black and the path of a 0.5" end mill around the part is shown in green.  The points of intersection of the end mill's centerline path are determined by:
1) Defining the lines in black as described above, and
2) Specifying an offset of 1/2 of the end mill's diameter in the Offset  fields.  In this example the offset values are +/- 0.25.

The signs of the offsets (+/-) determine their direction.  In general, a positive offset is used when the relative direction of the required line shift is up.  A negative offset is used when the relative direction of the required line shift is down.  Vertical lines are an exception as an offset up or down has no meaning.  Therefore a positive offset shifts a vertical line to the right and a negative offset shifts it to the left.



Referring to Figure 4 the line offsets are as follows:
L1: -0.25
L2: +0.25
L3: +0.25
L4: +0.25
L5: +0.25
L6: -0.25

Figure 5 depicts offset directions in greater detail.