klackity said:Darken-Sol: Did you not read my post about simplexes (the generalization of tetrahedrons)?
It's been done before. Here's a wikipedia article on exactly what I told you about: http://en.wikipedia.org/wiki/Barycentric_coordinate_system_(mathematics)
The wikipedia article uses linear algebra, but you can define Barycentric coordinates using compass and straightedge constructions (I think).
But I don't think anyone here is going to bother explaining the geometry to you.
The x,y,z coordinates represent the three dimensions of length, width, and height. In order to fully describe the position and orientation of a 3D object, we need to know its location in all three dimensions. This allows us to accurately define the shape and size of the object in space.
No, using only two coordinates would only give us information about the object's position in a 2D plane. In order to fully describe a 3D object, we need to know its position in all three dimensions. Using only two coordinates would not give us enough information to accurately represent the object's shape and size in space.
The x,y,z coordinates correspond to the length, width, and height dimensions respectively. The x-axis represents the horizontal dimension (length), the y-axis represents the vertical dimension (height), and the z-axis represents the depth dimension (width).
The Cartesian coordinate system is a standardized way of representing points in space. It allows for precise and consistent measurements and calculations of 3D objects. It also allows for easy visualization and manipulation of 3D objects in computer graphics and modeling.
Yes, there are other coordinate systems that can be used to describe 3D objects, such as polar coordinates or spherical coordinates. However, the Cartesian coordinate system is the most commonly used and is often preferred for its simplicity and ease of use in mathematical calculations.