It still seems to me like there is still redundancy here. If we were to store all vertices and edges as in a typical graph, couldn't we do a breadth first search to determine all of the triangles? In practice is this just computationally too expensive (while it might remove some redundant info it wouldn't be much)?
yzyz
I don't think that just storing the vertices and edges as in a typical graph is less redundant. Since we care about the orientation of the triangles (clockwise vs counter-clockwise), the edges should be directed. Then each directed edge would be used by one triangle, as the neighboring triangle, assuming it is oriented in the same direction, would use another edge directed in the opposite direction.
horrorsheep
I just wonder that is it necessary to store the vertices in the counter-clockwise order? What is the reason for that?
jsc723
I think sometimes we consider the counter clockwise order as frontside and the clockwise order as backside. So that the triangle can have an orientation
fywu85
To add to jsc723, I think oriented triangles are very useful when it comes to 3D geometry. For example, you can easily check if a point is inside or outside of a ball by only checking the face of a triangle from the mesh (assuming it is consistent in orientation) of the ball. A point inside the ball sees the vertices in clockwise direction, whereas a point outside the ball sees the vertices in counter clockwise direction.
It still seems to me like there is still redundancy here. If we were to store all vertices and edges as in a typical graph, couldn't we do a breadth first search to determine all of the triangles? In practice is this just computationally too expensive (while it might remove some redundant info it wouldn't be much)?
I don't think that just storing the vertices and edges as in a typical graph is less redundant. Since we care about the orientation of the triangles (clockwise vs counter-clockwise), the edges should be directed. Then each directed edge would be used by one triangle, as the neighboring triangle, assuming it is oriented in the same direction, would use another edge directed in the opposite direction.
I just wonder that is it necessary to store the vertices in the counter-clockwise order? What is the reason for that?
I think sometimes we consider the counter clockwise order as frontside and the clockwise order as backside. So that the triangle can have an orientation
To add to jsc723, I think oriented triangles are very useful when it comes to 3D geometry. For example, you can easily check if a point is inside or outside of a ball by only checking the face of a triangle from the mesh (assuming it is consistent in orientation) of the ball. A point inside the ball sees the vertices in clockwise direction, whereas a point outside the ball sees the vertices in counter clockwise direction.