What is the easiest way to calculate hidden faces of an cube

[JoeJoe]

Hello,


What is the easiest or fastest way to calculate which faces are covered by a cube.
If the cube rotates only around one axis, you can determine this simply by the angle, for example a>180° face 1,2,3,4 are not visible.
How does the whole thing look like if you rotate the cube on several axes. As far as I understood you have to determine the vector of the face. Then you have to calculate the angle of the vector to the observer. If this angle is greater than 90° the face is not visible. But this kind of calculation correct?

This is how my cube looks like until now.


Thanks
JoeJoe

[Thomas Richter]

Originally Posted by JoeJoe

How does the whole thing look like if you rotate the cube on several axes. As far as I understood you have to determine the vector of the face. Then you have to calculate the angle of the vector to the observer. If this angle is greater than 90° the face is not visible.

If you mean "hidden" instead of "covered", then this is correct. Compute the angle between the surface normal vector and the vector that points into the Z direction, i.e. the observer direction. Since that is just given by the arccos of the scalar product of both vectors, it is sufficient to look at the Z coordinate of the surface vector.


Depending on how you normalize your view vector, it is thus sufficient to check whether this coordinate is positive (pointing towards the observer) or negative (pointing into the opposide direction).


However, this works only if the surface has no holes. In general, you sort the surfaces from front to back, i.e. by the Z coordinate of its center, and then draw them from back to front. This always works.

[DanScott]

https://www.cubic.org/docs/backcull.htm

[JoeJoe]

Thanks for the information. I will implement it and then report when i have success.

[deimos]

If you plan on more complex objects than cubes (i.e. anything not a single purely convex object) then you may want to look at Binary Space Partitioning (BSP) trees next. This uses the surface normal work that you're about to do, but also gives you the order in which to draw the surfaces, rather than just using the painters algorithm (drawing from back to front) which only works in simple cases.

[JoeJoe]

It´s work now

[Antiriad_UK]

JoeJoe, which method did you end up using? My code has always used the 2D way but I recently added multi-point light sources so had to dig into all the normal/dot product math. No matter which way I tried to code it the 2D method was always faster for me.

My notes from the time were concerned with doing visibility check, followed by calculating normal for the visible face for lighting.

Rotate a point 3-axis: 			9 muls
Working out surface normal:	 	6 muls
Working out normal magnitude:		3 muls, 1 sqrt
Normalizing (dont have magnitude): 	3 muls, 1 sqrt, 3 divs
Normalizing (already have magnitude): 	3 divs
Working out dot product of unit vectors	3 muls
Face visibility check/2d method:	2 muls
Face visibility check/3d method:	9 muls (surface non-unit normal + dot product (sign only))

muls = 70 cycles
divs = 158
sqrt = 500

2D vs 3D Face Visibility
========================
As in all methods we end up doing the surface normal for visible faces is it quicker
to do the 2D check first and then only do the surface normal? Again assuming 20 faces, with
8 being visible on average.

Face 2D:
2d visibility check (20 faces)				2 * 20 muls
get surface normal for lighting visible faces (8 faces)		6 * 8 muls
							88 muls, 6160? cycles

Face 3D:
get surface normal (20 faces)				6 * 20 muls
3d visibility check,dot product with first vertex (20 faces)		3 * 20 muls
Get surface normal for lighting visible faces FREE
						180 muls, 12600? cycles
No contest. Use 2D method.

Another method I've seen is to just calculate the surface normal before you start drawing and rotate that new point along with all the other vertices but that's 9 muls per vertex. Looking at my notes in hindsight I've not included the perspective function in those calcs (2 shifts + 2 divs or 2 shifts + 1 div + 2 muls) - but can't off the top of my head think of how to skip that in the 3d method for only doing it on visible faces. In the end I calculated the surface normal magnitude once (or every time the object changed) and stored that with the face. Then doing 2d visibility check followed by lighting using pre-stored normal magnitude to remove sqrt. Be good if any of you vector geniuses can says how to do it better

[JoeJoe]

Sorry for the delay. I use the "old 2D" way from post 3 to do this.