In addition to displaying spatial figures and surfaces, the Euler3D spatial geometry construction software enables editing these objects with a high degree of mathematical control. (Filtering out self-intersections, inspection of planes, dissecting concave polygons into triangles)

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Spatial coordinate system

The program’s largest data unit is the project. Figures in the project are defined by their vertices, edges and sides. Vertices are defined by their coordinates (X, Y, Z), edges by selecting their starting and end vertices, sides by listing their defining vertices. In addition to using numeric coordinate values, the user can use constants, previously imported into the project (defined by the letters of the English alphabet).

Personalization

To help in the overview of an object, different transparent layers can be assigned to the vertices, edges and sides of the object. These layers can be turned on and off. In addition to the default numbering, the vertices, edges and lines can be tagged, and these tags can also be turned on and off to achieve the best view. The program uses perspective and axonometric (orthogonal) projection to display the objects. Two light sources are available for a realistic appearance. These can be fixed to a given point, or set to follow the camera movement.

Spatial transformations

Reflection across a plain, translation, rotation about an axis or stretching along axes can be carried out sequentially, as a product of several transformations. By setting the parameters, complex transformations, such as rotation around a chosen edge, or reflection across a side can be achieved.

Using the transformations allows for faster construction of polyhedra, since the coordinates of the vertices do not have to be given individually. By reflecting, translating or rotating the first specified vertices, the software automatically calculates the coordinates of the other vertices.

Built-in applications

Euler3D allows for the production of solids of revolution, such as cones or spheres. The duals can also be generated by applying polarity to the sphere. The animations make it possible to demonstrate complex spatial connections (e.g. the deduction of the tetrahedron’s volume) in a more comprehensible way. One of the program’s greatest strengths is its compatibility with other mathematical programs (Maple, Mathematica). The completed figures can be exported in several formats - a few file types even allow for the reading of data.

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