#heightmap

The idea of a heightmap is that rather than simulating the full volume of a fluid you only simulate its surface. Each cell on the horizontal grid represents a column of fluid. This particular algorithm is very simple: every timestep, each cell averages the heights of its adjacent cells, subtracts its own, and sets that number as its rate of height change. Basically, if a cell is lower than its neighbors, its height will increase; if a cell is higher than its neighbors, its height will decrease. Unity-wise, I just have a bunch of stretched-out cubes and every frame I set their vertical position to the height of the corresponding cell in the algorithm (which is why the wave pattern is replicated on the top and bottom). The algorithm runs every frame.

Now that I’ve sufficiently bored you, here’s some more videos:

This grid has a higher resolution, 100 cells to a side rather than 41. Of course, because it's a big square, that means there's 10,000 cells rather than 1,681 cells, and that's enough of a difference to cause a slowdown. Without the capture software the mid-resolution simulation runs smoothly, but the high-resolution one judders a little either way.

Part of the reason it's slow is just the larger quantity of cells; because the cells only check their neighbors' heights, the height "signal" can only travel one cell per frame, so even between frames was constant it would still take twice as long for the ripple to reach the edge. But the time between frames also increases because there are 5 times as many things to do.

I'll admit I'm a little disappointed. This was the simplest possible algorithm and it gets slow at only 10,000 cells. I want to get into much more realistic--and more complicated--realtime simulation. That sort of thing does exist, though, so all this really means is my implementation is bad. It was even slower at first--"unrolling" some boundary-checking and being smart about my for loops sped it up a lot. I'm sure there's more code optimization to be done. Furthermore, I'm not exactly a master of Unity--I'm sure there's much better ways to process and render fluids than re-assigning the position of thousands of transforms every frame. In fact, I'm currently working on replacing all the cubes with a single mesh, which should hopefully be faster. I'd love to use shaders, eventually, but that gets complicated quickly and I don't know how much interaction I can do with shader-simulated fluids.

You're bored again! I know! Here's it at 16 to a side.

Weird behavior here! The heightmap doesn't conserve "volume" I guess. It kinda shudders upwards. Does it always go up? The way I create the ripple is by setting the center cell's rate of height change to 2. Effectively I'm firing a pellet upwards from the center of the fluid. What if I set the rate of height change to -2--fire the pellet downwards?

Hah! The whole field goes down instead! There's an alternate way to achieve the ripple effect, though--I set the height of the center cell directly, rather than its rate of change. I'm lifting a column of water and letting it fall back down.

Huh. No significant change. Same when I push the height down rather than up. I guess the change in height dissipates more quickly than the change in velocity? The height change has to have some effect, but I guess it's small enough that there's no perceivable vertical change by the heightmap. By the way, I'm sure this change in median height happens to the higher resolutions as well, but because the amount of cells is higher the impact of a single cell's difference dissipates even quicker. I bet there's a mathematical reason for the difference in the effects of height change vs velocity change but I don't know how to find it.

Starting off simple and with only adjusting the Albedo (Colour), how reflective an item is (Metallic Slider) and how much micro detail an object has (Smoothness Slider) our 1st task was to make gold, silver, bronze and copper.

                                                      My Results

Taking what we learnt from here and building on previous knowledge of texture making the next challenge was making stone, with the addition of a normal and a height map. Which enable the materials shader to add some extra roughness and height to a surface without adding any extra to the polygon count of a mesh by adjusting the way light interacts and bounces off of a surface

    Stone Texture                        Normal Map                              Height Map

                                                      All together

Emission maps were next, these tell the shader not to include the area in light calculations, instead, the area will act as if it is a source of light.

 Brick Texture             Normal Map               Height Map               Emission Map