Geodesics on a rotating sphere - geodesic-sphere

I know when we live on a rotating sphere we feel virtual forces.By these forces how can we define our geodesics?l think these geodesics are different with the geodesics of a non rotating sphere.

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How do I find the corners of a plane in 3d space if I know three points

Apologies in advance for my feeble maths.
I'm trying to be able to find the corners of a plane in space based on the equation of that plane. Here's what I know. I know three points on the plane and I know where they fall in the 2d coordinate space of the plane (x,y) and where they are in 3d space. I know the width and height of the plane and I can now calculate the equation of the plane. The plane sits on the inside of a large sphere that surrounds the origin so, in theory, it should more or less face where the camera is (though in my diagram it doesn't face the origin as it's just for illustrative purposes)
But it's not clear to me how I can use that to figure out another point. One thought I had was to find the transform that moves the plane parallel to the xy axis and rotate it round one of the points (so it stays in the same place), find the position of the new point, and then rotate it by the inverse of that transform. But it's not clear to me how I would find that transform matrix or how to use it. Could I do this using the normal and vector maths? I understand what normals are, but I'm fuzzy about how to use them.

How to make squared patches on a shape smooth?

I'm implementing area light in my ray tracer. In a simple sphere obj model (i.e. it's the sphere that consists of triangles) squared patches are displayed. How can I make sphere surface smooth?
I suspect that surface normals calculation must be fixed.
Currently for each triangle single normal is computed for all points it contains.
Here's the sphere:
The square patches are displayed because you are simply seeing the triangles that make up the obj model. Either find an obj model with more triangles or use texture mapping to smooth the surface. If you are looking for a computationally effective method for drawing spheres, you can create a collision algorithm for spheres. I do not know how low-level you went on your ray-tracing project, but if you defined the reflection algorithm for the triangle, you can pretty easily do one for a sphere. I have created a visualization here:
https://www.geogebra.org/m/g9rrhttp
You can check that out if you want. If you do not want to implement this new algorithm, you can look for an obj model with a texture. the texture is what will make it appear smooth.

Z-fighting. Inaccurate coordinates of faces / shakes

For sufficiently large approaching the surface of the sphere, which is a model of the Earth, I get inaccurate coordinates of vertices. Because of this, when moving the camera the shaking noticeable.
How to get rid of it? On the Internet to find solutions to invert zNear and zFar, but I have no idea how to do it in three.js
THREE.PerspectiveCamera has near and far parameters. These define the distance of the near and far clipping plane.
You have to choose clipping planes depending on your scene. For example if you have a large scene, and the near plane is very small, it can cause things you experienced.

THREE Light 360 degree

How to make light which is lighting like SUN in the Space, that's mean from one center point in the middle of scene evenly in all directions.
Spotlight has limited angle
Directional light is not possible to use in both directions from the star sides.
Only idea I had is to positing a huge number of spotlights in one position rotated to all directions, butthis is not optimal solution, not CPU, GPU cost safe..
A THREE.PointLight casts light in all directions.

ray intersect planes with dynamic geometry returns empty array

* SOLVED *
It was not about 0,0,0 or distortion. It´s super weird but I found out that compute geometry as a Sphere worked! (even at the tiles corners, where you should think a sphere wouldnt cover it does)
http://threejs.org/docs/#Reference/Core/Geometry
computeBoundingSphere();
Problem desc. follows below.
Hey I'm building a webgl wall for my portfolio site, I need ray intersection to know both when user hovers over the wall and when they click what plane they're clicking on so I can redirect them to correct project.
http://www.martinlindelof.com
What i do is adding all planes on xyz(0,0,0) then I'm using dynamic geometry to place out their vertices on a point grid that's affected by a repelling particle (using traer)
now when I'm doing ray intersect (using examples from threejs r49) I get an empty array back, nothing hit.
could this be because all planes origins are in 0,0,0. should I maybe on each frame not only moving vertices but the entire plane?
or is something else.
(face normals seems to be pointing in the right direction, I see the texture on the plane and it's not inverted as it should be if it was the face backside with double sided planes. guess it's not by default in three.js when creating plane)
Ray got problems with object position 0,0,0 (because somewhere will be divided by position and will result in not dividable). Try another position.

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