~Maths ans Logic Fundamentals (Dot and Cross Product)~

Following on from the introduction to vectors, comes the Dot and Cross products.

The Dot and Cross products both consist of vector multiplication.

The Dot product results in a scalar product and it's used to calculate light Intensities and shadows in CG.

The cross products results in a vector product and it's used to calculate surface normals in CG.

Dot Product:

The dot product can be calculated in 2 different ways, by using the Polar Coordinates or by using the Cartesian Coordinates.

The Polar Coordinates involves multiplying the magnitude of a and b and the cosine of whatever the angle may be in the situation you're in.

The Cartesian Coordinates involves multiplying the the x lengths and the adding them to the result of multiplying the y lengths.

Note that if the vectors are at a right angle from one another then the Dot Product will always be 0.

Cross Product:

Once again, the Cross Product can be calculated using the Polar Coordinates and the Cartesian Coordinates.

Working out the Cross Product using Polar Coordinates is almost exactly the same as working out the Dot Product using Polar Coordinates only now, along with multiplying a, b and the cosine of the angle, you must now also multiply by the unit vector. The Unit Vector us simply another vector going at a right angle from both a and b.

Working out the Cross Product using Cartesian Coordinates involves multiplying and subtracting by the x, y and z dimensions in different formations in order to find the 3 new dimensions, giving you the cross product.

The order you must both multiply and subtract the dimensions of a and b by to get the new dimensions.