### 9 Constructions

The following is valid for all constructions: Either select the base-objects for your new object first and then press the corresponding button, or use ’New object’ and click on the base-objects afterwards. If the buttons are not hidden, the texts on the buttons change in reaction to the selected objects such that you always see what’s constructed.

The following section shows, sorted by object-type, all possible constructions and the necessary parent-objects. These possibilities also appear as tooltips for the corresponding buttons / symbols.

The easiest way to get an overview of the possible constructions is to give the commands in the ’New object’-menu a try.

• Plane:
1. through three points
2. through a point on the plane and normal vector
3. through a point and a perpendicular line
4. through a point and two direction vectors
• Parallel: through three points in the order vertex - apex - vertex. For a detailed example see the Chapter ’First steps’.
• Triangle: Select three vertices. For triangles with textures the first vertex is the bottom left corner of the texture, the second the bottom right and the third is on the top middle. This can be changed afterwards in the texture-coordinate-setting.
• Vector: By start- and endpoint. The vector is then drawn to point from the first to the second point. Though vectors theoretically can be freely translated, the position must be determined for Archimedes to know where to paint it.
• Line:
1. through two points
2. as intersection of two planes
3. as perpendicular line to a plane through a point
• Dependent point:
1. free on a line
2. free on a plane
3. free on a sphere
4. free on a circle
5. intersection of line and plane
6. intersection of line and line
7. intersection of circle and circle
8. intersection of line and sphere
9. intersection(s) of line and circle
10. intersection of three planes
11. As the intersection of an arbitrary object with a line: See subparagraph Schnitte.
• Free point: Generates a free point in the origin. Double-right-click generates a free point behind the mouse-pointer.
• Sphere:
1. By midpoint and point on the sphere
2. By midpoint and a vector giving the radius of the sphere. This comes in handy when the radius is defined elsewhere, the vector does not need to start at the sphere’s midpoint!
• Circle: Take a moment to consider that a circle in space is not given by midpoint and a point on the circle only. The plane the circle lies in must be given, too.
1. by midpoint, point on circle and normal vector (such that the circle lies in the plane perpendicular to the normal vector).
2. by midpoint, point on the circle and plane.
3. by midpoint, vector giving the radius and normal vector. This is useful if the radius shall be defined elsewhere.
• Model: Loads a 3D-model from a file. This can be a model made with Archimedes (format .osg or .ive) or a model in a well known format like .3ds or .x. The model can be freely positioned, rotated and scaled within the scene.

This function is useful for putting together a scene from several pieces. Be aware of the fact that you cannot edit the parts of a model, this can only be done using macros, see the introduction to macros and the chapter about macros.

• Normal: Draws the perpendicular line to a plane through a given point.
• Locus surface: See chapter ’Locus surfaces’
• Vector sum (V1+V2): Generates a vector as the sum of two given vectors.
• Vector difference: (V1-V2): Generates a vector as the difference of two given vectors.
• Zylinder: When selecting two points and a vector Alt - s or the segment-button will generate a cylinder the axis of which will go from the first to the second selected point and whoose radius is given by the length of the selected vector.

Two points and an expression result in a cylinder, too. The radius is given by the expression.

• Intersection:
1. Arbitrary object with plane: An arbitrary object (even locus surfaces, groups or models can be used) will be intersected with a plane and an intersection-curve will be generated. This way of computing an intersection-curve works with the graphical representation of the objects, not with the mathematical definition. Thus, the more accurately the objects are drawn, the more accurate the intersection-curve will be. If you intersect a locus-surface with a plane, be sure not use too few supporting points for the locus.
2. Arbitrary object with line: Arbitrary objects (see above) can be intersected with lines here. This makes sense to compute the intersection of a line with a triangle or parallelogram, too. The user will have to decide himself how many intersections should be computed. When moving objects there will be no check for continuous movement of the intersection points. This will result in sudden jumps of points when for instance the first intersection of a line and a surface ceases to exist after the movement and thus the second intersection will become the first instead.