Geometry Nodes, Displacement, and the Implicit Tree

If you already think in Geometry Nodes, the Objects tree is the graph. A Mesh Boolean is a hard CSG node: vertices, then a cut. The purple diamond on that same Boolean turns the branch into a signed distance field. Blends, offsets, and lattices stay live on the field. A hard tab still belongs here as CSG. You do not keep the blend in another window.

What you will learn: how a Geometry Nodes graph maps onto the Objects tree; when Mesh Boolean stays CSG; when the purple diamond is the implicit tree; and where Blender displacement lands: the Heightmap Warp node for an image, Surface Pattern for a procedural relief, or a level-set offset.

This is a map, not the field mathematics. Signed Distance Fields: Geometry as a Function is that article.

A Geometry Nodes tree is a program over mesh (or over fields that become mesh). Set Position, Mesh Boolean, Realize Instances, and Named Attributes all land on vertices, edges, and faces.

Rig Cad evaluates the same program as an Objects tree. The kernel is the difference.

• Leave the Boolean as CSG and you get Mesh Boolean: a crisp cut, coincident faces that can fail, and a mesh you can remesh later.
• Click the purple diamond and the descendants become a field. Union is min, difference is max(A, -B), and smooth is a blend whose width and profile (quadratic, cubic, circular fillet, chamfer, stairs) you pick under Blend Mode. The surface is where the field is zero.

Shade Smooth in Blender is shading. SDF smoothness is geometry.

Diagram: stay on CSG for a hard cut; switch the Boolean to SDF when the next step is a blend, an offset, or a lattice.

flowchart LR
  A["Mesh Boolean habit"] --> B{"Need a blend, offset, or lattice?"}
  B -- No --> C["Keep the branch as CSG"]
  B -- Yes --> D["Purple diamond, SDF branch"]

Table: Geometry Nodes and modifiers next to Rig Cad.

Difference is still ordered. The first child is the body you keep. Later children are cutters. That is Mesh Boolean's first / second socket, not a bag of solids.

Two solids and an operation is the first Geometry Nodes boolean you ever built. That playground is here. Switch union, difference, intersection, and hull on the same pair. This is CSG. The tree is the pretty-printer.

A mounting tab, a hole, a tray wall: stay on this kernel. You do not send the simple cut back to a mesh editor.

The node you already know can evaluate as a field. In the Objects tree, click the purple diamond on a Boolean. Its descendants turn purple and pick up SDF options: smooth for a rounded blend, and Precision on the root of that branch. Descendant precision values do not override the root.

That is the Geometry Nodes moment where people reach for a voxel remesh plus a Smooth modifier, or a downloaded SDF node group. Here the blend is the operation, not a cleanup pass.

The showcase below keeps a mesh branch and an SDF branch in one tree: a hard difference on the mesh kernel, and under it a smooth union (the node colored yellow in the viewport) that blends a box with a gyroid-filled sphere. That is the hybrid. Use the field where the blend or lattice matters. Keep the crisp feature as CSG.

In Blender, Displace and Set Position take a mesh and move its vertices along a normal or a vector field. The resolution is the mesh. Subdivide, then displace. Voxel remesh if the topology tears.

Rig Cad has that operation. Heightmap Warp (Operations 3D → Deformation) takes one geometry child—union several upstream first—a grayscale image, and a projection frame: Cartesian, cylindrical, spherical, toroidal, triplanar, or cubic. Direction displaces along the frame axis or along each vertex's Surface Normal, which is the classic displacement-map behavior. Intensity is world units at white; Symmetric keeps mid-grey neutral so a knurl or grip does not inflate the part; Top and Bottom Angle Masks keep print tops and bed faces flat; Refinement subdivides before warping, because a sharp primitive still needs tessellation to carry the detail. It is the Displace modifier with the print-prep options built in.

An implicit tree adds two moves that have no vertices at all. An offset of $c$ is $\phi = c$. That is the neighboring level sets in the SDF article, not a modifier stack; every node in an SDF branch has a Surface Offset option for it, and a post-process Surface Offset still exists for solved geometry, the way Solidify exists after the node tree. And Surface Pattern, a field-only post-processing step, embosses or debosses any of 150+ procedural patterns into an SDF surface with a chosen depth and fillet—the closest analog to a procedural texture displace, but live on the field and never dependent on mesh density.

Image-driven density, thickness, and morph on a 3D pattern (a gyroid, a Schwarz D) are the other analog to a texture displace: the field is modulated, then meshed. That is not the same as painting a heightmap onto an arbitrary solid and hoping the mesh holds. For the pattern itself, start at Gyroid TPMS.

Table: Blender habits next to Rig Cad.

Keep the hard cut as CSG. Switch the branch when the next operation is a blend, an offset, or a lattice. Oversize the Cutter is the coincident-face and thin-cut article for both kernels. Post-Processing in Rig Cad is the ordered stack—Shell, Mirror, Cut Plane, and the field-only Infill and Surface Pattern—that sits where your modifier stack used to. Mesh Cleanup is what you do after the field becomes triangles.

You already think in a graph. Signed Distance Fields: Geometry as a Function is the field, the eikonal, and how Precision is chosen. Gyroid TPMS is the lattice you would have built as a volume, and Pattern 3D: Lattices, Infill, and Surface Textures is the full catalog of those patterns with the bounding recipe and the cost measurements. When the field is slow to mesh, Why Is My Model Slow? is the diagnostic; Realize Instances maps onto the repeat nodes in Repeats and Arrays.

Constructive Solid Geometry in Rig Cad is the long form of the Boolean table. If the editor panels are new, Rig Cad Editor Guide is the five-panel map. The same kind of map exists for Tinkercad, Fusion 360, OpenSCAD, and Onshape and SolidWorks.