1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
|
# Useful links
## Constrained dynamics
- [A lot of pictures to get general idea and familiarize, but not very understandable](https://danielchappuis.ch/download/ConstraintsDerivationRigidBody3D.pdf)
- [More text and math but very well written and understandable](https://graphics.pixar.com/pbm2001/pdf/notesf.pdf)
## TODO:
- Camera perspective rendering:
- Subspace intersection
- Instead of orthogonal projection, intersect camera plane with the ray (S2 x S1 interesection)
- Scale radius:
- Take a right-most point (particle.pos + camera.right * true_radius)
- Project this point
- projected(radius) = projected(particle.pos) - projected(right_most_point)
- More generic `fn draw_sphere(radius, world_pos)`
- Implement vector drawing for debug:
- Line + small dot at the end
- Display particle forces
- Display particle velocities
- Display jacobians for each constraint (render constraint jacobian at each related particle)
- (?) Toggleable gradient for each constraint:
- Artificially take C(q) with some grid
- Grid should be on a plane, need an ability to control this plane as well
- (?) Refactor: subspace distance constraint:
- beam = distance to point
- slider = distance to a line
- But constraint has to act on 1 particle and 1 subspace, I will need dynamic subspaces (from point)
- Hold this for now
### Better scene design
What defines a scene:
- List of particles - points with mass that are affected by gravity
- List of global forces (gravity, drag, etc.)
- List of other renderable objects: beams, springs, lines, planes (each object may depend on some particle position):
- Each object may depend on particle position or some static point (line passing through a particle, spring between particle and static point)
- Each objects knows how to compute its subspace (point/line/plane)
- Beams automatically add constraints to particles
- Springs automatically register extra forces between particles
- Collision planes setup necessary routines
- List of additional constraints between particles and subspaces (e.g particle tied to a line)
<!-- - List of subspaces (special points, lines, planes etc.) - used as connectors for constraints -->
<!-- - (?) List of dynamic subspaces based on particle positions (i.e a plane that passes through a particle) -->
- Camera spec (lens etc.), position and orientation - defines how the scene is projected on the picture plane
What the we should see on the screen:
- Particles (rendered as spheres with some small radius)
- Subspaces - points, lines, planes(?)
- Some constraints (beams represented as lines)
- Some forces (like springs)
|
