oh boy… this is going to be a frequent topic. i *hate* how vector fields are drawn. i don’t believe i’ve ever seen a vector field drawn well. ever. why? [hello matlab, mathematica, et al…]
square grid sampling: yuk.
non-adaptive sampling: too few samples near equilibria & too many where the vectors are large
long vectors intersect: yuk.
the arrows are drawn poorly. also, yuk.
no/poor use of color.
static pics — vector fields should induce flow (in your mind)
can i fix all these problems? hardly. not easily. but i’m trying. here’s an early attempt. it, too, is flawed. but notice the difference that a hex grid, a bit of style on the arrows, a little 3-d layering, and some ambient occlusion make.
this overhead still from BLUE 2 chapter 17 is a decent effort: the soft shadow maps on the base plane are warm & undistracting. the contrast between the surface shader and the contour lines is also a win. when animated, this is not bad.
here’s an early picture that i drew for BLUE vol 2 chapter 1: it’s a simple surface, with cel shading and a nice (though primitive) color palette. some things work. i like how the base plane accepts shadows & helps frame the figure in 3-d. in retrospect, i should have used soft shadows instead of hard & the specular on the cel shading is distracting. it looks a bit better animated.
but — it’s the hidden lines and countours that tell the real story. see that cusp singularity? there’s a lot of mathematics hiding in a single figure.