Posts tagged gif
Posts tagged gif
lotr meme: 3/8 QUOTES
“All that is gold does not glitter, not all those who wonder are lost; The old that is strong does not wither, deep roots are not reached by the frost.
From the ashes a fire shall be woken, a light from the shadows shall spring; Renewed shall be blade that was broken, the crownless again shall be king.”
The wave equation
The famous second order linear partial differential equation, known as the wave equation, describes the behaviour of all sorts of waves, including acoustic and electromagnetical:
The visualization was an exercise in solving differential equations numerically. It shows the interaction of waves generated from two point-like sources.
This equation is tiny, elegant, yet powerful: its simple form hides both the wondrous phenomena of resounding strings of an instrument, and the play of light on the surface of a pond.
(I didn’t know how to make the waves not to reflect at the edges of grid. But then I figured out: a shore. Waves are dissipated as the sea floor raises gently - the damping is progressively higher on the edges. Is there a better way to simulate an infinite grid?)
Rotation Illusion - Torus Knot 23
I was cleaning my hard drive and I found some of my old projects. That’s what I did when I learned how to do particle effects.
Rapidly-Growing Random Tree (RRT) path planning algorithm
There are things that are easy to do for humans, and really hard to do for robots. One of such things is the problem of path planning - how to find a path between the start and the goal, and avoid the obstacles in between?
There is a wide range of methods employed precisely to solve this problem. There are path planners basing on potential field methods, Wavefront planners, roadmap algorithms, and so on. Each of them has its specific advantages and shortcomings.
RRT algorithm is one of such planners. It’s based on a randomized approach, making it only probabilistically-complete. The idea is to grow (extend() method) two trees at start and goal locations, and try to find a connection (connect() method) between them, as the trees continue to explore the space.
The RRT algorithm was introduced in the paper Rapidly-Growing Random Tree (RRT) path planning algorithm by James Kuffner and Stevan LaValle. The whole idea is explained there in detail.
Path planning allows you to find a path between obstacles in a configuration space. It doesn’t have to be a 2 dimensional one, or even 3 dimensional. It can consists of many dimensions: the generalized coordinates (like robot arm joint angles, speed, even temperature). The method can also be a subject of various modifications.
I tried to make a simple explanation of Extend() and Connect() in the first two gifs. In Connect() method, you may have to perform a lot more steps before you find the connection.