point projection into yx rotated plane

Question

I want to simulate depth in a 2D space, If I have a point P1 I suppose that I need to project that given point P1 into a plane x axis rotated "theta" rads clockwise, to get P1'

It seems that P1'.x coord has to be the same as the P1.x and the P1'.y has to b shorter than P1.y. In a 3D world:

cosa = cos(theta)
sina = sin(theta)
P1'.x = P1.x
P1'.y = P1.y * cosa - P1.z * sina
P1'.z = P1.y * sina + P1.z * cosa

Is my P1.z = 0? I tried it and P1'.y = P1.y * cosa doesn't result as expected

Any response would be appreciated, Thanks!

EDIT: What I want, now I rotate camera and translate matrix

EDIT 2: an example of a single line with a start1 point and a end1 point (it's an horizontal line, result expected is a falling line to the "floor" as long as tilt angle increases)

I think it's a sign error or an offset needed (java canvas drawing (0,0) is at top-left), because my new line with a tilt of 0 is the one below of all and with a value of 90º the new line and the original one match

Answer 1

The calculation you are performing is correct if you would like to perform a rotation around the x axis clockwise. If you think of your line as a sheet of paper, a rotation of 0 degrees is you looking directly at the line.

For the example you have given the line is horizontal to the x axis. This will not change on rotation around the x axis (the line and the axis around which it is rotating are parallel to one another). As you rotate between 0 and 90 degrees the y co-ordinates of the line will decrease with P1.y*cos(theta) down to 0 at 90 degrees (think about the piece of paper we have been rotating around it's bottom edge, the x axis, at 90 degrees the paper is flat, and the y axis is perpendicular to the page, thus both edges of the page have the same y co-ordinate, both the side that is the "x-axis" and the opposite parallel side will have y=0).

Thus as you can see for your example this has worked correctly.

EDIT: The reason that multiplying by 90 degrees does not give an exactly zero answer is simply floating point rounding