Thread by @FreyaHolmer

A little thread on generating and rendering a procedural trajectory mesh! #madewithunity #unity3d

Trajectories under constant linear acceleration, gravity in our case, has a simple equation

p = p₀ + v₀t + ½gt²

p = Position
p₀ = Initial position
v₀ = Initial velocity
t = Time
g = Gravity

To get the velocity v at any given point, we derive the formula to get

v = v₀ + gt

Quite usefully, this vector is tangent to the curve! When normalized, it represents the direction of motion at any given time. In our 2D case, we can also get the normal by rotating it 90°

So here's my "concept art" for what I wanted the trajectory mesh structure to look like! One long quadstrip through the center, with perpendicular quads along the whole thing at equal time intervals. Both the tangent and the normal are used in positioning each of these vertices!

Now, procedural meshes are often defined on the CPU, but calculating all of this on the CPU is a bit of waste. After my initial test, it hit me that all of this math, could be done in the vertex shader instead, that way we don't have to update the mesh data every frame anymore 🎉

So instead of calculating each vert on the CPU and writing that to the mesh data every frame, we generate the mesh *once*! Part of this involves making sure the GPU has all data on what vertex is where in its local quad. For example, here's the code for the perpendicular quads

This all means we can now provide the constants (p₀, v₀ and g) through a material property block, while the time value and vertex local positioning info is in the vertex UV data, so the GPU/shader can do all the positioning work ✨

A quirk with GPU vertex positioning is that frustum culling will use the bounds of the mesh data rather than that of the rendered positions of each vertex. You *could* do the CPU math for its real bounds, or just, you know

make it cover the observable universe and call it a day

This was created earlier on stream - I'm also going live right now, come hang out! I always try to keep things educational, so feel free to ask anything at any time 💖

twitch.tv/acegikmo