Ai does not build 3D models like you do (implicit models)

The most popular way to create a 3D model is by placing sets of faces, edges and vertices (surfaces, lines, curves and points) within your 3D modeling software. Faces, edges and vertices make up a type of model called a B-rep, or Boundary Representation. This is standard for Solidworks, AutoCAD and Blender. You define the limits that represent the boundaries of your model. Ai typically does not generate B-reps, instead they make Implicit models.

Implicit models have existed since the 1960s, but you may not know about them because they're a challenging specialized tool. They are comprised of math functions to achieve a 3D model. 

There are no faces, edges or vertices; there is only surface.

Here's an example of how to make a sphere using a B-rep or Mesh: 

In Solidworks, you can create a sphere by using the sphere tool under "Features." The sphere needs to have a radius of 1000mm, so you edit it with the dimensions tool. A sphere's defined limits can also be Mesh. The difference is that Mesh divides surfaces into a finite number of triangles where B-reps use rectangles and polygons.

Here is an Implicit model function to generate a sphere with a 1000mm radius: 

[ f(x, y, z) = x^2 + y^2 + z^2 - 1000mm ]

It's coding for 3D models. 

These functions can even be written in Python or C++. And you might bother to write it with a programming language, as opposed to directly into Implicit modeling software like Autodesk ShapeMaker, in order to automate parts of the process. The reason why Ai uses Implicit modeling is because it's more efficient (particularly if you can do math as fast as a computer). 

There are benefits like:

Smaller file size

Faster render time

More robust to small errors in data

Smoother curves for a wider variety of shapes

Generating partial surfaces (for medical imaging)

Sharp edges are better represented as non-convex objects

If you aren't inclined to math and coding, it's foreign to think about what an Implicit model is made of regarding real life. The word "implicit" doesn't help given it has several meanings. It's intended to say that the surfaces of objects can be defined by math, with absolute accuracy, and without points or lines.

These models are held together by "applied math" and "pure math," so if it feels a little theoretical, that's because it is. Instead of thinking in 3D, let's think of a 2D Implicit model.

If you remember math class in grade school, despite trying to forget, you'll remember learning to plot points and draw lines on a graph. Let's say the assignment is to make a blue square by (1) plotting 4 points so that you can (2) draw 4 lines and then (3) color within the lines with blue crayon. 

But math is dumb and you want to get this over with. Instead, you skip some steps because you already know where the blue square is going to go just by looking at the plot points. So, you draw a blue square on the graph without points or lines. You kept the boundaries in your head, so the square has no bounds.

Building upon that, Topography uses Implicit models. Even though it's a map of Earth, something real and tangible, the process of mapping landscape doesn't use points or lines. And contour lines can only express visual information about a surface, not the bounds defined as an edge.

Implicit models are on the rise due to Ai. It's unlikely we will need to learn to write them, but it's a good idea to know how to interpret them.

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