Contents
Can a stereographic projection miss one point on the sphere?
Although any stereographic projection misses one point on the sphere (the projection point), the entire sphere can be mapped using two projections from distinct projection points. In other words, the sphere can be covered by two stereographic parametrizations (the inverses of the projections) from the plane.
How is a spherical projection obtained in Blender?
A spherical projection is obtained with the very explicit “Sphere Projection”. What matters here is that the 3D cursor is perfectly at the center of the sphere or else the projection is totally deformed. Here is what I did with 2 spheres: For “Project from View”, I simply unwrapped the 2 halves separately.
Can you use UV coordinates to make a planar projection?
Of course there is. It has nothing to do with UVs though. Object coordinates give you x, y and z coordinates of any object you choose. Take only any two axis that you need and you get a planar projection.
How is a Cartesian grid distorted in stereographic projection?
In Cartesian coordinates a point P(x, y, z) on the sphere and its image P′(X, Y) on the plane either both are rational points or none of them: A Cartesian grid on the plane appears distorted on the sphere.
Why is 3D projection on a 2D plane problematic?
If some detail has a z coordinate smaller than d, it is basically between the window and the eye. These are problematic, because projecting them to the window no longer makes sense wrt. optics.
What is the outline of a smooth surface under a projection?
The outline of a smooth surface under a central projection is the intersection with the image plane of rays from the viewpoint (camera center) that are tangent to the surface. For a quadric surface described by the symmetric matrix Q, the resulting curve has a fairly simple representation in terms of dual conics/quadrics.
Why does 3D projection hurt the eye in real life?
If any graphical primitive, like a line, plane, or sphere, intersects with the eye, it means the eye is badly hurt in real life; with 3D projection, we get unrealistic results (like polygons getting twisted through origin), because our model breaks down at the eye point.
What is the goal of exercise 2 stereographic projections?
LAB Exercise #2 Stereographic Projections GOAL: Stereonets are a convenient and common way to represent structural orientation data. This lab will give you practical experience using stereonets to plot your structural data. In this lab you will get experience plotting by hand and using software for the problem set.
How to calculate the dip in a stereographic projection?
1) Rotate the tracing paper such that the two ends of the great circle that represents the plane are at North and South. 2) To determine the dip, count the grid squares from east or west 3) Make a tick mark on your tracing paper on top of the North from the stereonet.
How is stereographic projection carried out in a computer?
In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereographic net, shortened to stereonet, or Wulff net . Illustration by Rubens for “Opticorum libri sex philosophis juxta ac mathematicis utiles”, by François d’Aguilon.