f₃

Scalar Field Lab

Explore functions of three variables in 3D

1Function & Domain

Example

f(x,y,z)

x min

x max

x samples

y min

y max

y samples

z min

z max

z samples

2Visualize the 4th Variable

Geometry shows where you are in 3-space; color and slices show the scalar value f(x,y,z).

z = current slice y = current slice x = current slice point sample cloud color volume

Slice opacity

Point sphere size

Point cloud opacity

Color volume transparency

The color volume fills the whole viewing box. Its six boundary faces show heat maps of the field; transparency lets you see the colored interior.

Color min

Color max

symmetric color scale about 0

3Level Surfaces

highlighted level attach to current point show level stack color level surfaces wireframe surfaces

Highlighted level c

Stack min

Stack max

Interval

Stack transparency

Resolution

Stack starts almost entirely transparent (10% opacity). Moving the slider right makes the stack less transparent / more opaque. Neighboring level surfaces can be neutral gray or colored by value.

4Gradient & Normal

gradient vector ∇f unit normal vector tangent plane to level surface leave probe trail

Tangent-plane size

Plane opacity

Plane color

Turn on the tangent plane to display its equation.

gradient vectors on highlighted level

Surface vector count

Surface vector scale

Surface vector thickness

Vector scale

Finite-difference h

5Display & Navigation

axes ground grid domain box orthographic camera

Scalar field

xanimate x

yanimate y

zanimate z

Drag: orbit · Shift/right-drag: pan · Wheel: zoom