There are two types of geometry in geometry, one is explicit geometry and the other is implicit geometry. There are different ways to represent different geometries
implicit geometry
Implicit actually means that it does not tell you where the specific points are, it only tells you the relationship that these points satisfy. Represents a certain relationship but does not give the actual point.
Example:
implicit geometric representation.
The disadvantage is that it is difficult to see the geometric shape represented by the above formula.
The advantage is that it can judge whether a point is on this geometry.
explicit geometry
Explicitly, a triangular surface is directly represented by points, and there is another surface defined by the method of parameter mapping. For example, the
input UV is mapped to a certain point in space, and a function is defined to give you UV output (x , y, z)
example
: UV is mapped into actual points in space (x, y, z).
It becomes difficult to judge whether a point is geometrically correct or not.
Some applications of implicit geometry
Through some simple Boolean operations to form a complex geometry
Through distance function operations
For any geometry, it does not directly describe its surface, but to describe the shortest distance from any point of it to this surface.
The resulting distance function formed by fusing the geometric
distance function refers to the minimum distance between any point in space and any point on the geometric shape you want to represent. This distance can be positive or negative. If It is considered that there is a point outside the geometric surface, then the minimum distance of this point is calculated and then added with a positive sign, that is positive, if there is a point inside the geometry, then the minimum distance from this point to the surface of this geometry, And this distance is considered to be negative. That is to say, define a value for any point in the space, calculate the distance functions of the two objects, and then fuse the two distance functions, and then restore the original object to get the following transformation Here is
an example of applying the distance function.
The actual example of the distance function.
How to restore the surface after the distance function is fused.
It is actually difficult to find out all the distance functions equal to 0.
Alternative method: the grid (level set)
level set that stores the approximate value of the function It doesn’t have to be defined in two dimensions, it can also be defined in three dimensions . There is also
a special description method Fractals (fractals).
Some applications of explicit geometry
The point cloud
does not consider that the object is a surface, but a bunch of points on the surface. Each point is represented as a point. As long as these points are represented fine enough, the gaps between points will not be seen naturally. Do some Scanning of three-dimensional space
polygon mesh
is more commonly used, such as three-dimensional modeling software
