In the movie Pi, Max says mathematics is the language of nature, and everything can be represented and understood through numbers. This might not be entirely true, but where Game Development or VFX are concerned, the difference between a hobbyist and a professional lays in the fundamental insights in what you're doing - and sometimes this comes in the dreaded form of... maths.

DAE students get a solid introduction to mathematics and how it applies to their areas of interest.This includes functions, trigonometry, vectors and matrices, all applied to relevant topics. One of the exercises we start with, is using matrices (and vectors) to understand the way computers translate a virtual 3D world, made up of vertices and polygons, into a 2D screen space, made up of pixels. Concepts like World and Object matrix are clarified and combined with Camera and View Matrix to end up with a demo as seen below.

1_math_world_camera_view from DAE on Vimeo.

Another area where mathematics is key: lighting and rendering. Nowadays everybody is talking about PBR, or Physically-Based Rendering.

To prepare our students for these topics, we first take a step back and have a look at the basics of specular, diffuse and reflection, starting out by calculating diffuse, reflection and half-vector specular. In the next video you see the application of how we use normal, camera and light vectors to visualise the half-vector.

2_math_halfvector_reflection from DAE on Vimeo.

Below you can see how we are using 3DS Max and shaderfx to illustrate band shading. 3DS Max allows the use of high level blocks, but here we focussed on the fundamentals instead, and as such, most of the shader is made up of matrices and vector calculations.

3_math_dot_cros_matrix_toonshader from DAE on Vimeo.

4_mat_dot_cros_vector_matrix_reflectionshader from DAE on Vimeo.