CODEWITHSUNDEEP
cmathmatrix3drotation
Jacob Brunson
Jacob Brunson

Reputation: 1492

How to render 3D axes given pitch, roll, and yaw?

I'm attempting to render a simple axes display like the following, except using simple 2D lines.

axes

I have angle values for the pitch, yaw, and roll that the axes should display. (e.g. PI/2, PI/4, PI*3/2)

I have a function that can render 2D lines given start and end points in 2D space.

How can I properly render a rotated set of axes given the angles? I don't care about z-indexing (so if sometimes the lines incorrectly show up on top of each other, that is OK as long as they point the correct direction).

What I've tried

I know that the start points for all the lines will just be in the center of the axis, and we'll say the center is at (0, 0) and the length of the axes will be 100. That leaves me to calculate the endpoints for each of the 3 axes.

I have defined the X axis to be left-to-right, the Y axis to be up-and-down and the Z axis to be back-forward (i.e. out of the screen).

Pitch is rotation around the X axis, roll is rotation around Z axis, and yaw is rotation around Y axis.

To calculate the X-axis end point I've done:

x = cos(roll) * cos(yaw) * 100;
y = sin(-roll) * 100;

To calculate the Y-axis end point I've done:

x = cos(roll + PI/2) * 100;
y = sin(-roll - PI/2) * sin(PI/2 - pitch) * 100;

To calculate the Z-axis end point I've done:

x = cos(PI/2 - yaw) * 100;
y = sin(PI - pitch) * 100;

It's probably evident that I don't really know what I'm doing. I feel like I am taking a very naive approach when I should be using something more advanced like matrices. If it makes a difference, I'm using C, but psuedocode is fine. Any help would be appreciated.

Upvotes: 2

Views: 4209

Answers (1)

Nico Schertler
Nico Schertler

Reputation: 32667

First, you need to agree on an order of the rotations. In the following, I assume the order x, y, z (pitch, yaw, roll).

The end points are simply the column vectors of the according rotation matrix. Then, you need to project the 3d points onto the 2d screen. It seems as if you use a simple orthogonal projection (removing the z-coordinate). So here are the results:

x1 = 100 (cos yaw * cos roll)
y1 = 100 (cos pitch * sin roll + cos roll * sin pitch * sin yaw)

x2 = 100 (-cos yaw * sin roll)
y2 = 100 (cos pitch * cos roll - sin pitch * sin yaw * sin roll)

x3 = 100 (sin yaw)
y3 = 100 (-cos yaw * sin pitch)

Upvotes: 3

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