Using measure feature, you can find the distance between two points or a point and a lineal, as well as angle between two lineals (in case lineals are intersected) or distance between them (in case lineals are not intersected). GeomSpace uses unusual Measure Dialog due to the fact different spaces have different configurations of mutual positions of lineals. GeomSpace measure obtains only relevant informations and all these informations. They include measure characteristic (showing what kind of measure it is) and measure value (direct and complementary). It is important to know both direct and complementary values because for some measure characteristics one of them can be infinite or unmeasurable (for details, please refer to theory behind GeomSpace: “Uniform Theory of Geometric Spaces” or “Analytic Geometry of Homogeneous Spaces”, available at project cite).
In order to explane what means relevant and non–relevant informations, consider two lines on Euclidean plane. In case they are intersected, the most relevant information is the angle between them (elliptic measure characteristic). In case they are parallel, the most relevant information is distance between them (parabolic measure characteristic). If these two lines are on elliptic plane, there is no difference between distances and angles as all measures have elliptic characteristic. If these two lines are on hyperbolic plane, they can be intersected (elliptic measure characteristic), parallel (parabolic measure characteristic) or divergent (hyperbolic measure characteristic). All these cases are properly handled by measure feature.
You can open Measure Dialog (Figure 8) by pressing Measure button from Calculate group. Using Construct Chooser, you can fill out Lineal 1: and Lineal 2: outputs by pressing Lineal 1, respective Lineal 2 buttons. They may form some existing or new faces. After that, press Calculate button to find relevant measure characteristic and value between lineals.