Basic Matcap

This is the most basic matcap projection. Its a representation of normals relative to the camera. For a Sphere the matcap projection is basically just screen space that tracks with the object (can be useful in other contexts too).
If you want to use an image texture as your matcap, you first need to remap from (-1 : 1) to (0 : 1) like this.
On a sphere, the texture will look undistorted you can make a bad Fresnel effect with matcap mapping.
Or you can create crispy procedural matcaps to make for example NPR metal shaders or like in this case create a "mask" to mix in lighting, color and stepped gradient effects.