From the course: Introduction to 3D

What is geometry?

From the course: Introduction to 3D

Start my 1-month free trial

What is geometry?

“

- 3D objects are virtual, they only exist as numbers in a computer. These numbers define the objects and their surface. We often refer to these surfaces as geometry because they're defined by the mathematics of geometry. Now I'm not going to get too technical, but let's look at how geometry defines a surface. In a 3D application, we have to break down a surface into its component parts. These parts are triangles. Triangles or chosen because, by definition, they're flat. Remember three points determine a plane. So no matter how I try to deform this triangle, it retains its shape. Any other shape may not remain flat. This rectangle for example can bend and it doesn't retain its shape. So we can't be exactly sure which direction its surface is facing. The reason we need a flat surface is so that we know exactly what direction it is facing. This is called the normal. So for this, the normal is perpendicular to the plane of the triangle. When we know the direction of the normal, then we can calculate how this part of the surface will interact with light. Understanding surface direction is how we visualize the surface in a computer and ultimately render an image. So the triangle is a fundamental unit of a surface in 3D. How we get to triangles may be a little more complex. The most basic way is to simply build the surface out of triangles. This however may get messy when the surface gets more detail. To get around this, we can create a simpler surface that resolves to triangles. One way is to use rectangles or polygons to build the surface. Each polygon then automatically resolves to triangles. We can further abstract the surface by using less detail. When that detail is subdivided, it becomes a smooth surface. This technique is called a subdivision surface. Another common method is to create patches, which define a surface along a curve. These again resolve to triangles through a technique called tesselation. Now there are other methods for creating surfaces, but regardless of how we abstract the surface, the ultimate result will be triangles. So now that we understand the basics of how surfaces are created, let's look at some common techniques for creating them.

Contents