Parametric Geometry¶

Elementa's geometry system is built on top of the gmsh OpenCASCADE kernel, wrapped by ElementaCAD.

Parameters¶

Before creating geometry, define symbolic parameters in Definitions → Parameters.

Name    Expression   Description
W       0.1          Width (m)
H       0.05         Height (m)
r       W/4          Radius

All geometry dimension fields accept expressions that reference these parameters. Parameter expressions may use:

Arithmetic: +, -, *, /, **
Standard math functions: sin, cos, sqrt, exp, log, pi, e, …
Other parameters: W/2, 2*r, H + gap

Parameters are resolved with full dependency tracking — you can define gap = W * 0.1 and then use gap elsewhere.

2-D Primitives¶

Rectangle¶

A centred rectangle with specified width and height.

Parameter	Description	Default
`dx`	Width	`1.0`
`dy`	Height	`1.0`
`cx`	Centre X	`0.0`
`cy`	Centre Y	`0.0`

Boundaries are automatically tagged as <name>_edge_0 … <name>_edge_3.

Disk (Ellipse)¶

An elliptical disk.

Parameter	Description	Default
`rx`	Semi-axis X	`0.5`
`ry`	Semi-axis Y	`0.5`
`cx`	Centre X	`0.0`
`cy`	Centre Y	`0.0`

Polygon¶

An arbitrary closed polygon defined by a list of vertices.

Parameter	Description	Default
`points`	List of `(x, y)` tuples	`[(0,0),(1,0),(0.5,0.8)]`

Example expression: [(0,0), (W,0), (W/2, H)]

3-D Primitives¶

Box¶

Parameter	Description	Default
`dx`, `dy`, `dz`	Dimensions	`1.0` each
`cx`, `cy`, `cz`	Centre	`0.0` each

Faces are tagged <name>_face_0 … <name>_face_5.

Sphere¶

Parameter	Description	Default
`r`	Radius	`0.5`
`cx`, `cy`, `cz`	Centre	`0.0` each

Cylinder¶

Parameter	Description	Default
`r`	Radius	`0.2`
`h`	Height	`1.0`
`cx`, `cy`, `cz`	Base centre	`0.0` each

Boolean Operations¶

Boolean operations combine multiple primitives into a new shape. The input primitives are consumed (removed from the model tree) and replaced by the result.

Union¶

Merges two or more shapes into a single domain.

result = A ∪ B ∪ C

Difference¶

Subtracts subsequent shapes from the first.

result = A − B − C

Tip

Use Difference to cut holes in a surrounding domain — essential for multi-domain problems such as a conductor embedded in a dielectric.

Intersection¶

Retains only the region common to all input shapes.

result = A ∩ B

Boundary Tagging¶

After each primitive or boolean operation, Elementa automatically creates named physical groups for all resulting boundaries. These names appear in the boundary condition assignment panel and the gmsh .msh file.

Primitive	Boundary names
Rectangle	`<name>_edge_0` … `_edge_3`
Disk	`<name>_edge_0`
Box	`<name>_face_0` … `_face_5`
Boolean result	`<name>_bnd_0`, `<name>_bnd_1`, …