Tutorial P: Waffle canopy

Video	Grasshopper Tutorial For beginners (YouTube, channel Rhino Grasshopper)
Application	Algorithmic Modeling (Katydid)
You learn	Mirroring in a plane, merging points into a curve, a surface from boundary curves, contours, offset and ruled surfaces, extruding by a computed thickness
Sizes	Millimetres: a 58 × 70 profile, a 90 mm span, 13 ribs 4 mm deep

The canopy grows from one curve. Its mirror gives the far side, two arches close it at the bottom and the top, a surface spans the four, and parallel slices of that surface become the ribs.

Step by step

1. The profile

The video draws half of the profile in Rhino’s Front view and references it into a Curve parameter. Katydid cannot reference a FreeCAD sketch yet, so the profile is drawn on the canvas instead: five Construct Point components, their X and Z typed with right-click › Set value…, all wired into one Interpolate with Shift held, so they arrive in order.

2. The Bottom and Top points

Two more Construct Points stand in for the two Rhino points: Bottom (X 14, Y 45) sets the mirror plane and the bulge at the base, Top (X 44, Y 20, Z 84) the height and depth of the top arch. Sliders move them, as the Gumball does in Rhino.

3. Mirror

Mirror with the profile in G, the Bottom point in P and the normal N typed 0, 1, 0: the mirror plane is the XZ plane through the Bottom point. Grasshopper builds that plane with an XZ Plane component; Katydid’s Mirror takes the point and the normal itself. Dragging Half span now widens or narrows the canopy.

4. End points

Four Evaluate Curve components with t = 0 and t = 1 give the start and end of both curves (Grasshopper’s End Points; Katydid’s t always runs from 0 to 1).

5. The two arches

Bottom arch: the profile’s start, the Bottom point and the mirror’s start, Shift-wired into an Interpolate in that order. Several wires into one input merge their data in order, as Grasshopper’s Merge does.
Top arch: the same through the Top point projected onto the mirror plane. Two Deconstruct components and a Construct Point take the Top point’s X and Z and the Bottom point’s Y.

The bottom and top arches closing the outline

6. The surface

The video spans the four curves with Edge Surface, which Katydid does not have yet. A Loft through three sections stands in: the profile, a middle section from the Bottom point through the profile’s midpoint to the projected Top point, and the mirror. It passes through both arches at their middle, where the bulge is.

The canopy surface lofted through three sections

7. Contours

Contour the surface along Y: N typed 0, 1, 0, and D a Series of plane offsets. The span is the Distance between the two start points; an Expression divides it by the Count slider (12), and an Addition gives count + 1 planes: 13 ribs.

The video subtracts 0.001 from the spacing so the last slice is not lost on the edge. Katydid’s Contour cuts a fine mesh, where a plane that close to the edge splits into fragments, so the first and last planes sit 1 mm inside instead.

Thirteen contour curves across the surface

8. Rib strips

Offset Curve moves each contour by the Rib depth (4 mm) in its own plane. Ruled Surface spans each contour and its offset, both inputs Flattened (right-click › Flatten), so the curves pair up one to one.

Flat strips between the contours and their offsets

9. Thickness

Multiplication of the spacing and a Thickness ratio slider (0.3) gives the rib thickness, Vector XYZ turns it into a Y vector, and Extrude gives the strips their thickness: 13 solid ribs.

10. Bake

Select the Extrude and click Home › Algorithm › Bake: the ribs become 13 Part solids in the Part Navigator. Katydid has no Custom Preview colours yet, and there is nothing to internalise, since the profile is on the canvas.

The replay

#	In the book (NX)	In FreeCAD NX-Style	Result	Notes
P1	Rhino’s Front view; open Grasshopper	Ctrl+N + Application > Algorithmic Modeling	same	an empty canvas on the new part
P2	Draw half of the profile in Rhino’s Front view; Curve > Set one Curve	stand-in: five Construct Points (X and Z typed with Set value…) Shift-wired into Interpolate	missing	profile from Vector (0.0, 0.0, 0.0) to Vector (58.0, 0.0, 70.0), length 108.4 mm. Katydid has no Curve parameter that follows a FreeCAD sketch yet (asked for): the points are typed instead of drawn
P3	Two Rhino points, Bottom and Top, referenced into Point parameters (moved with the Gumball)	stand-in: two Construct Points driven by sliders	missing	bottom Vector (14.0, 45.0, 0.0), top Vector (44.0, 20.0, 84.0); sliders move them, as the Gumball does in Rhino
P4	XZ Plane at the Bottom point; Mirror the curve in it	Mirror: G = the profile, P = the Bottom point, N typed 0, 1, 0 (Katydid’s Mirror takes the plane as a point and a normal)	differs	mirrored profile at y = 90.0; the span is twice the Bottom point’s Y
P5	End Points of both curves	stand-in: Evaluate Curve at t = 0 and t = 1 on each	missing	{'s0': (0.0, 0.0, 0.0), 'e0': (58.0, 0.0, 70.0), 's1': (0.0, 90.0, 0.0), 'e1': (58.0, 90.0, 70.0)}. Katydid has no End Points component yet (asked for); Evaluate Curve’s t runs from 0 to 1 along the curve
P6	Bottom arch: Merge (start, Bottom point, mirrored start) into Interpolate; top arch the same through the Top point Projected onto the mirror plane	Merge: the three points Shift-wired into Interpolate’s V in order; Project stand-in: Deconstruct the Top point, its Y replaced by the Bottom point’s	differs	arches pass through the Bottom point and the projected Top point at (0.0, 0.0) mm. Shift-wiring several sources into one input merges them in order (Grasshopper does the same); Katydid has no Merge or Project component yet
P7	Edge Surface from the four boundary curves (a loft would ignore the arches)	stand-in: Loft through the profile, a middle section (Bottom point, the profile’s midpoint on the mirror plane, the projected Top point) and the mirrored profile	missing	surface area 9023 mm^2; it passes through the Bottom point and the projected Top point ((0.0, 0.0) mm), so it follows the arches at their middle. Katydid has no Edge Surface yet (asked for)
P8	Contour the surface along Unit Y; distance = span / count (Distance, Division); edge fix x - 0.001	Contour with N typed 0, 1, 0 and D = a Series of offsets: 1 mm, then (span - 2) / count apart, count + 1 of them, so the first and last planes sit 1 mm inside the edges	differs	13 contour curves for count 12, 7.333333333333333 mm apart; per plane [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]. Katydid’s Contour takes one plane offset per item, so a Series lists them; Division is an Expression here
P9	Offset Curve by the rib depth; Ruled Surface between each contour and its offset (both Flattened)	Offset Curve with a 'Rib depth' slider; Ruled Surface: A = the contours, B = their offsets, both inputs Flattened (right-click > Flatten)	same	13 flat rib strips, 19395 mm^2 in all
P10	Extrude the strips along Y by spacing x a thickness ratio (Multiplication, Unit Y)	Multiplication (spacing x 'Thickness ratio' 0.3) into Vector XYZ’s Y, into Extrude’s D	same	13 solid ribs, 41284 mm^3; thickness [2.2] mm (spacing 7.333333333333333 x 0.3 = 2.2000)
P11	Custom Preview with a Colour Swatch	-	missing	Katydid previews everything in one colour (red, green when selected); per-component colours are not there yet (asked for)
P12	Bake the ribs; Internalise the referenced curve	select Extrude + ribbon 'Home › Algorithm > Bake'	same	13 rib solids in the Part Navigator, 41284 mm^3. Nothing to internalise: the profile’s points are typed on the canvas, not referenced

In the book (NX)

In FreeCAD NX-Style

Result

Notes

Rhino’s Front view; open Grasshopper

Ctrl+N + Application > Algorithmic Modeling

same

an empty canvas on the new part

Draw half of the profile in Rhino’s Front view; Curve > Set one Curve

stand-in: five Construct Points (X and Z typed with Set value…) Shift-wired into Interpolate

missing

profile from Vector (0.0, 0.0, 0.0) to Vector (58.0, 0.0, 70.0), length 108.4 mm. Katydid has no Curve parameter that follows a FreeCAD sketch yet (asked for): the points are typed instead of drawn

Two Rhino points, Bottom and Top, referenced into Point parameters (moved with the Gumball)

stand-in: two Construct Points driven by sliders

missing

bottom Vector (14.0, 45.0, 0.0), top Vector (44.0, 20.0, 84.0); sliders move them, as the Gumball does in Rhino

XZ Plane at the Bottom point; Mirror the curve in it

Mirror: G = the profile, P = the Bottom point, N typed 0, 1, 0 (Katydid’s Mirror takes the plane as a point and a normal)

differs

mirrored profile at y = 90.0; the span is twice the Bottom point’s Y

End Points of both curves

stand-in: Evaluate Curve at t = 0 and t = 1 on each

missing

{'s0': (0.0, 0.0, 0.0), 'e0': (58.0, 0.0, 70.0), 's1': (0.0, 90.0, 0.0), 'e1': (58.0, 90.0, 70.0)}. Katydid has no End Points component yet (asked for); Evaluate Curve’s t runs from 0 to 1 along the curve

Bottom arch: Merge (start, Bottom point, mirrored start) into Interpolate; top arch the same through the Top point Projected onto the mirror plane

Merge: the three points Shift-wired into Interpolate’s V in order; Project stand-in: Deconstruct the Top point, its Y replaced by the Bottom point’s

differs

arches pass through the Bottom point and the projected Top point at (0.0, 0.0) mm. Shift-wiring several sources into one input merges them in order (Grasshopper does the same); Katydid has no Merge or Project component yet

Edge Surface from the four boundary curves (a loft would ignore the arches)

stand-in: Loft through the profile, a middle section (Bottom point, the profile’s midpoint on the mirror plane, the projected Top point) and the mirrored profile

missing

surface area 9023 mm^2; it passes through the Bottom point and the projected Top point ((0.0, 0.0) mm), so it follows the arches at their middle. Katydid has no Edge Surface yet (asked for)

Contour the surface along Unit Y; distance = span / count (Distance, Division); edge fix x - 0.001

Contour with N typed 0, 1, 0 and D = a Series of offsets: 1 mm, then (span - 2) / count apart, count + 1 of them, so the first and last planes sit 1 mm inside the edges

differs

13 contour curves for count 12, 7.333333333333333 mm apart; per plane [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]. Katydid’s Contour takes one plane offset per item, so a Series lists them; Division is an Expression here

Offset Curve by the rib depth; Ruled Surface between each contour and its offset (both Flattened)

Offset Curve with a 'Rib depth' slider; Ruled Surface: A = the contours, B = their offsets, both inputs Flattened (right-click > Flatten)

same

13 flat rib strips, 19395 mm^2 in all

P10

Extrude the strips along Y by spacing x a thickness ratio (Multiplication, Unit Y)

Multiplication (spacing x 'Thickness ratio' 0.3) into Vector XYZ’s Y, into Extrude’s D

same

13 solid ribs, 41284 mm^3; thickness [2.2] mm (spacing 7.333333333333333 x 0.3 = 2.2000)

P11

Custom Preview with a Colour Swatch

missing

Katydid previews everything in one colour (red, green when selected); per-component colours are not there yet (asked for)

P12

Bake the ribs; Internalise the referenced curve

select Extrude + ribbon 'Home › Algorithm > Bake'

same

13 rib solids in the Part Navigator, 41284 mm^3. Nothing to internalise: the profile’s points are typed on the canvas, not referenced

Result	Means
same	The book’s NX steps work as written.
differs	It works, but the FreeCAD way is different; the notes say how.
limit	The book’s way fails in FreeCAD itself; a workaround follows in the next steps.
missing	FreeCAD has no such function; a stand-in follows.
skipped	Not replayed; the notes give the reason.
FAILED	Did not work.

Result

Means

same

The book’s NX steps work as written.

differs

It works, but the FreeCAD way is different; the notes say how.

limit

The book’s way fails in FreeCAD itself; a workaround follows in the next steps.

missing

FreeCAD has no such function; a stand-in follows.

skipped

Not replayed; the notes give the reason.

FAILED

Did not work.