#Rules for rotation in geometry how to
#Rules for rotation in geometry full

The point at which we do the rotation, we'll call point P. Well, let's say the shape is a triangle with vertices A, B, and C, and we want to rotate it 90 degrees. The shape is being rotated! But how do we do this for a specific angle? With your finger firmly on that point, rotate the paper on top. Now place your finger on the rotation point. Put another paper on top of it (I like to imagine this one as being something like a transparent sheet protector, and I draw on it using a dry-erase marker) and trace the point/shape. Here's something that helps me visualize it: The 'formula' for a rotation depends on the direction of the rotation.

I'm sorry about the confusion with my original message above. If you want to do a clockwise rotation follow these formulas: 90 = (b, -a) 180 = (-a, -b) 270 = (-b, a) 360 = (a, b). Also this is for a counterclockwise rotation.

#Rules for rotation in geometry full

360 degrees doesn't change since it is a full rotation or a full circle. 180 degrees and 360 degrees are also opposites of each other. So, (-b, a) is for 90 degrees and (b, -a) is for 270.

Since vectors represent directions, the origin of the vector does not change its value.The way that I remember it is that 90 degrees and 270 degrees are basically the opposite of each other. Because it is more intuitive to display vectors in 2D (rather than 3D) you can think of the 2D vectors as 3D vectors with a z coordinate of 0. If a vector has 2 dimensions it represents a direction on a plane (think of 2D graphs) and when it has 3 dimensions it can represent any direction in a 3D world.īelow you'll see 3 vectors where each vector is represented with (x,y) as arrows in a 2D graph. Vectors can have any dimension, but we usually work with dimensions of 2 to 4. The directions for the treasure map thus contains 3 vectors. You can think of vectors like directions on a treasure map: 'go left 10 steps, now go north 3 steps and go right 5 steps' here 'left' is the direction and '10 steps' is the magnitude of the vector. A vector has a direction and a magnitude (also known as its strength or length). In its most basic definition, vectors are directions and nothing more. If the subjects are difficult, try to understand them as much as you can and come back to this chapter later to review the concepts whenever you need them. The focus of this chapter is to give you a basic mathematical background in topics we will require later on. However, to fully understand transformations we first have to delve a bit deeper into vectors before discussing matrices. When discussing matrices, we'll have to make a small dive into some mathematics and for the more mathematically inclined readers I'll post additional resources for further reading. Matrices are very powerful mathematical constructs that seem scary at first, but once you'll grow accustomed to them they'll prove extremely useful.

This doesn't mean we're going to talk about Kung Fu and a large digital artificial world. There are much better ways to transform an object and that's by using (multiple) matrix objects. We could try and make them move by changing their vertices and re-configuring their buffers each frame, but that's cumbersome and costs quite some processing power.

#Rules for rotation in geometry how to

We now know how to create objects, color them and/or give them a detailed appearance using textures, but they're still not that interesting since they're all static objects. Transformations Getting-started/Transformations