Introduction
Modes
MonGeo provides two modes of operation:
- Projection mode
- Algebraic mode
The following sections describe the characteristics of each mode in detail.
Projection mode
In this mode only points, and lines can be created. The points and lines created in this mode are projections and traces of geometric objects, not the objects themselves. In this mode, one must take care to associate the pairs/triplets of drawn projections to concrete geometric objects.
This mode is most useful when setting up a drawing from data given in the form of a problem statement.
This is also the most useful mode if one wants to construct every element "by hand".
Algebraic mode
In algebraic mode one can create points, lines and planes, given preexisting elements. Back-end algebraic rules are used for this purpose.
The construction of objects created in algebraic mode is not drawn. Only the desired object is drawn through its projections.
In Projection mode the projections imply the objects. In Algebraic mode the objects imply the projections.
Projection Mode Commands
In projection mode one is only allowed to draw points, lines and circles.
These points and lines are drawn in the plane of the observer/user (you), and they represent projections or traces of geometric objects on specified projection planes.
As they are drawn, the points and lines are not associated with any concrete object, they simply exist on their own. The association of projections and traces to form concrete 3D objects must be done explicitly.
Therefore, in projection mode, the projections and traces come first and they define the geometric objects implicitly.
Aliases for the Projection Planes
In projection mode, one must specify the projection plane in which one wishes to draw. For that purpose, when drawing/creating a new point, or line, one should press the associated character or number alias of the intended plane.
Here is the list of aliases of the projection planes:
v 0 View Plane
f 1 Frontal Plane
h 2 Horizontal Plane
p 3 Profile Plane
In what follows, the place-holder for the projection plane alias is defined as [pp], which in practice will be either the character or the number associated with the intended plane.
One may also omit the alias when issuing a command. In which case the new object will be drawn in the View Plane by default.
Drawing Points
We shall use the character . (point) as the trigger command to draw/create a new point.
[pp] . [line] [line] intersection of two lines.
[pp] . [circ] [line or circ] <Ctrl> Enter
intersection of a circumference and another
curve (line or circumference).
Optional Ctrl key to resolve ambiguity.
Drawing Lines
We shall use the character - (dash) as the trigger command to draw/create a new line.
[pp] - [point] [point] passing through two points.
[pp] - [point] [line] passing through a point at 90 degrees with a
line.
[pp] - [point] (angle) [line] <Ctrl> Enter
passing through a point at a specified angle
with a line.
Optional Ctrl key to resolve ambiguity.
[pp] - [line] (length) <Ctrl> Enter parallel at a distance (length) from a line.
Optional Ctrl key to resolve ambiguity.
Drawing Circumferences
We shall use the character < (open angle bracket) as the trigger command to draw/create a new circumference.
[pp] < [point 1] [point 2] center in point 1 and containing point 2.
[pp] < [point] (length) Enter center in a point with a given radus.
Labels
Every element that is drawn in projection mode is automatically given a label. This label is composed of 3 alphabetic characters. The generic format is given below using regular expression notation:
[a-zA-Z]{2}
Examples: Gf BK xg
Associating Projections to Actual Objects
Define a concrete point, line, circumference or plane using the name command, n:
n [point or line or circ] [point or line or circ] = [a-z][a-z][a-z]
The newly named object can be a point, a line a circumference or a plane.
Only named objects can be used/referenced in Algebraic mode.
Generic guidelines
- Lengths should be provided in cm (centimeters)
- Angles should be provided in degrees.
Algebraic Mode Commands
To find/create points
| Sequence | Description |
|---|---|
| g + "x" + "y" + "z" | Create a point given its components x, y and z. |
| g + (point1) + (point2) | Find the reflection of point1 about point2 |
| g + (point) + . + (point) | Find the midpoint between given points. |
| g + (point) + (line) | Find the point that is the reflection of given point about given line. |
| g + (line) + (plane) | Find the point of intersection between a line and a plane. |
| g + (line) + (line) | Find the point of intersection between the given concurrent lines. |
| g + (plane) + (plane) + (plane) | Find the point of intersection between three planes. |
| g + (point) + "d" + (line) | Find the 2 points at a distance d from given point that lie in given line. |
To find/create a lines
| Sequence | Description |
|---|---|
| r + (point) + (point) | Find the line that passes through the two given points. |
| r + (point) + . + (point) | Find the perpendicular bisector of the given points. |
| r + (point) + (line) | Find the line parallel to given line that contains given point |
| r + (point) + . + (line) | Find the line orthogonal (and concurrent) to given line that contains given point |
| r + (point) + (plane) | Find the line orthogonal to given plane that passes through given point. |
| r + (line) + (line) | Find the angle bisector between the given concurrent lines. |
| r + (plane) + (plane) | Find the line of intersection between the given planes. |
To find/create a plane
| Sequence | Description |
|---|---|
| v + (point) + (point) | Find the bisecting plane between the given points. |
| v + (point) + (point) + (point) | Find the plane that contains the given points. |
| v + (point) + (line) | Find the plane that contains given line and given point. |
| v + (point) + . + (line) | Find the plane orthogonal to given line that contains given point. |
| v + (line) + (line) | Find the plane that contains the given concurrent lines. |
| v + (line) + . + (line) | Find the bisecting plane between the given concurrent lines. |
| v + (plane) + (plane) | Find the bisecting plane between the given concurrent planes |
Other commands
| Sequence | Description |
|---|---|
| d + (object) | Delete object |
| h + (object) | Hide object |
| u | undo |
| Ctrl + r | redo |