Rotors are a rotation representation generalized from Quaternions and Complex numbers that works in any numbers of dimensions.

The article starts by pointing out that rotation is defined as a scalar property on a plane. The canonical representation of a plane is a bivector representing the outer product of two vectors. The bivector is in principle a fundamental concept just like the vector. Similar to how a vector represents a point with a scalar length, a bivector represents a plane with a scalar area (signed). The area of a bivector a∧b is |a||b|sin(angle). The reason we also see the term |a||b|sin(angle) from cross product is because cross product actually gives rise to a bivector instead a vector! Historically we've been confusing bivectors with vectors because they have the same representation in 3D.

The inner and outer product completes a geometric product of two vectors: ab=a⋅b+a∧b. Reflection R(a,v) is defined elegantly using geometric product: R(a,v)=-ava. Then it's noted that two reflections is equivalent to a rotation by twice the angle between a and b: R(a,R(b,v))=ba v ab. The "ab" here is known as a rotor. Applying a rotor on both sides of a vector rotates this vector in the plane a∧b by twice the angle between a and b. Quaternion is just a representation of Rotors in 3d: i:=y∧z, j:=z∧x, k:=k∧y. The scalar part (w in w+xi+yj+zk) corresponds to the inner product.

Keywords: bivector, geometric product, rotor, quaternion, rotation

Vulkan learning guide.

In-depth and low-level knowledge about GPU.

Normally when we implement ray tracing, each ray of light carries a RGB vector. Spectral Ray Tracing is the technique of instead of treating a ray of light as a particle in a straight line, the algorithm treats light as a wave spectrum - spectral power distribution (SPD). This allows more realistic rendering such as dispersion, diffraction, etc.

TIL signed distance field. First I need to explain the concept of alpha testing. Alpha testing is a rendering technique for textures. It dictates that when rendering a texture, perform a test on the alpha value of that pixel against a threshold. Completely throw out or keep the data depending on the comparison result. Typically the alpha value for each pixel is set to the actual transparency of the pixel. This signed distance field method calculates the signed distance of each pixel to the nearest color pixels. The signed instance field is then saved in alpha channel in the texture. All the remaining alpha-testing mechanism is the same. It's claimed that this technique improves the rendering quality of low-resolution textures drastically.

Read the original paper: https://steamcdn-a.akamaihd.net/apps/valve/2007/SIGGRAPH2007_AlphaTestedMagnification.pdf