An Attractor can be based on a set of points, or curves. Basically, this formula will form an expanding and evolving system based on how the values in the formula change. Let's talk about some more complex formulas, and the visualization practices that come with them.Ī Strange attractor is a mathematical field for dynamic systems. So nothing can be transformed or rotated without knowing the starting angle of it's position. Rotation involves angles and degrees in it's calculation. You'll notice every-time you use a Transform SOP, that it is also based around the origin in the scene. Rotation also relies heavily on right triangles. This is because the displacement of the Mountain SOP is based around the origin. If you move your geometry anywhere else in the scene besides the origin, you'll notice that the displacement will change. Using the Mountain SOP in Houdini would be a great way to visualize the displacement you are adding to points in your scene. The starting point being 0,0,0 in 3D space, and the end point being anywhere else. Vector displacement describes the shortest length of distance of a vector from it's starting position. Using this as the starting position for anything, you can suddenly figure out where everything aligns in 3D space using that as a starting angle. Which at the center (0,0,0), forms a perfect right angle. If you look at a graph you have the three dimensions X, Y, and Z in their proper planes. Vector displacement and rotation rely heavily on shape and attributes of right angles. You can pair audio channels using functions, blend them, or measure the angles of the audio waves in radians, degrees, or cycles.Īs I came out with the first draft of this article, two people pointed out that I should probably mention right triangles. It operates on the chosen inputted audio and allows you to chose which math function to apply to the channels. The Function Channel node is one of these. Therefore, they also contain channel VOPs, and other nodes to edit the audio. Because they operate with audio channels, they also operate with the wave frequency of the audio. You can also input these functions into parameters on your objects to control how their movement slows, smooths, or changes over time based on your chosen wave.ĬHOPs rely heavily on wave functions to operate. There are more functions, but these are just the basics. For example, acos would compute the arc of the cosine value, atan the arc of tan, and asin the arc of the sin value. Vops also contain there own trigonometric functions for calculating a curve. In V OPs you can use the Sin, Cos, Tan, or Oscillator nodes to build waves to feed into your attributes. You might notice that most of the tools in Houdini that are centered around these functions can be used in VOPs, CHOPs, or wrangles. However, the name name for trigonometry wouldn't come until the 4th century BC when it was named after the Greek work for measure: trigōnon. It's probably one of the oldest mathematical formulas out there, and has been used by the ancient Egyptians and Babylonians. Trigonometry has also been used since 2000 BC. These waves are incredibly useful in 3D space. These functions also produces wave like lines when you place them on a graph. Here is an easy way of remembering the formulas: For example, to calculate the angle called Sin, you'll need to find the length of the opposite side of the triangle, and the length of the hypotenuse and then divide them. Which are called the opposite, hypotenuse, and adjacent.
But I'll talk more about that below. Triangles have three sides. As the name suggests, these formulas are based of the angles of triangles. These are called Trigonometric functions. I won't be diving into VEX functions or scripting, but I will be covering the visualization of mathematics in the software. Now keeping this in mind, this article will be covering mathematical creations with Houdini, and the history behind them. These functions can also sometimes be scripted by you in wrangles. Houdini primarily uses a language called VEX to read inputted values and dependencies with functions you chose. No matter how different the attributes or values are in the formula, it will be Houdini's job to collect and calculate the information.
Houdini's core (no pun intended) is centered around the idea that every creation will be created from the basis of a mathematical formula. So I have been meaning to cover this topic for awhile.
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