You can construct new space by choosing its specification and color. When you press New button from Space group, the Space Dialog (Figure 2) appears. Space Dialog allows you to choose the dimension and, after pressing Change button, space specification as number of characteristics k1,k2,...,kn, where
Each characteristic may have one of the following values:
If you choose Euclidean, elliptic or hyperbolic (Bolyai-Lobachevsky) space of dimension n, use the following
specification {k1,k2,...,kn}:
{0,1,...,1} — for Euclidean space,
{1,1,...,1} — for elliptic space and
{−1,1,...,1} — for hyperbolic space.
If you plan to use another space use the algorithm presented in Figure 3 to determine its specification. For more
information about what space specification is about and how to find it, please refer to the theory behind
GeomSpace: “Uniform Theory of Geometric Spaces” (presented in popular manner) or “Analytic
Geometry of Homogeneous Spaces” (presented in rigurous mathematical manner), both available at the
project website.
Default values for space specification in Space Dialog is taken from previous space (or dimension 0 with no specification if no space was present). So you can clear the space just by pressing New button and accepting default values.
Choosing the Color. Beside space dimension and specification you can choose space background color. Space Dialog, as well as other dialogs, uses a simple color chooser for geometry elements, presented at Figure 2, at left picture in red border.
This element acts as toggle button. Four spinners for color components open/hide on its press. You can choose R (red), G (green), B (blue) and A (alpha, opacity) color components in range 0 ... 255. While modifying the color components, Color Chooser button changes its color to reflect the current color selection. Its central part shows color with opacity and outer part uses solid color in order to figure out the opacity by contrast.