Interpolate
Interpolate
Extrapolate
Intrapolation & Extrapolation
Sagrida Familia Schools Roof
Step 1 : Sine Wave
Step 2 : Decrease the point count, increase the wave frequency and amplitude
Step 3 : Multiple similar waves along the Y-axis
Step 4 : Nurbs Surface
Step 5 : Crest (from trough) at start of last wave
Step 6 : Flattening amplitude towards the middle
Step 7 : Trough Protrusion
Step 8 : Thicken
Sine Ribbon
```d
// Peak
height = 30;
coneStart = Point.ByCoordinates
(0,0,0);
coneEnd = Point.ByCoordinates
(0,0,height);
peak = GeometryColor.ByGeometryColor
(Cone.ByPointsRadius
(coneStart, coneEnd, 25),
Color.ByARGB(255,55,60,55));
// Coastline
coast = PolyCurve.ByPoints
(Point.ByCoordinates
([50,70,90,60,50,30,0,-50],
[-50,0,25,50,80,60,70,50]));
// Base
base = PolyCurve.ByPoints
(Point.ByCoordinates
([50,70,90,60,50,30,0,-50,-50],
[-50,0,25,50,80,60,70,50,-50]),
true)
.ExtrudeAsSolid(0.35);
baseClrd = GeometryColor.ByGeometryColor
(base,Color.ByARGB(255,200,200,135));
// Water
water = GeometryColor.ByGeometryColor(
Surface.ByLoft(
[coast,coast.Offset(300)]),
Color.ByARGB(50,75,205,235));
// Builing Mass
site = Rectangle.ByCornerPoints
(Point.ByCoordinates
([20,20,50,50],
[50,30,30,50]));
mass = site.ExtrudeAsSolid(20);
// Color Solid
GeometryColor.ByGeometryColor(mass,
Color.ByARGB(255,225,185,145));
GeometryColor.ByGeometryColor(coast.Extrude(0.5).Thicken(0.5),
Color.ByARGB(255,0,0,255));
// Sight Lines
eye = coneEnd;
coastVertices = coast.Points;
sightLines = Line.ByStartPointEndPoint
(eye, coastVertices);
```
#### Vantage
Considering the point at the top of the cone to be the eye level, plot lines from eye level the coast line vertices and loft these lines to create a surface.
```d
// Cutting Tool
cuttingTool = Surface.ByRuledLoft
(sightLines);
GeometryColor.ByGeometryColor(
cuttingTool, Color.ByARGB(200,190,190,190));
// Trim Solid
trimmedSolid = Solid.Trim
(mass,
cuttingTool,
Point.ByCoordinates(20,50,20));
// Color Solid
GeometryColor.ByGeometryColor(trimmedSolid,
Color.ByARGB(255,225,185,145));
```
#### Variation
The trimmed form is faceted as the cutting surface is created with a Ruled Loft
However if the cutting surface was created using a Loft, it would be smooth
#### Alteration
While retaining the same workflow and code, while only replacing Surface.ByRuledLoft with Surface.ByLoft, an alternate geometry is obtained
```d
// Cutting Tool
cuttingTool = Surface.ByLoft
(sightLines);
GeometryColor.ByGeometryColor(
cuttingTool, Color.ByARGB(200,190,190,190));
// Trim Solid
trimmedSolid = Solid.Trim
(mass,
cuttingTool,
Point.ByCoordinates(20,50,20));
// Color Solid
GeometryColor.ByGeometryColor(trimmedSolid,
Color.ByARGB(255,225,185,145));
```
#### Iteration
Further design development could involve geometry analysis and creation based on solids, faces, curves, points or normals obtained as a result of prior operations.
```d
// Cutting Tool
cuttingTool = Surface.ByRuledLoft
(sightLines);
GeometryColor.ByGeometryColor(
cuttingTool, Color.ByARGB(200,190,190,190));
// Top Surface
massExtents = mass.Intersect(cuttingTool);
// Thicken Surface
massThicken = massExtents.Thicken(-50,false);
// Trim Solid
trimmedSolid = Solid.Trim
(Solid.ByUnion(massThicken),
Plane.XY(),
Point.ByCoordinates(20,50,-20));
// Color Solid
GeometryColor.ByGeometryColor(trimmedSolid,
Color.ByARGB(255,225,185,145));
```
```d
cuttingTool = Surface.ByLoft
(sightLines);
GeometryColor.ByGeometryColor(
cuttingTool, Color.ByARGB(200,190,190,190));
massIntersect = mass.Intersect(cuttingTool)[0];
perimeterCrvs = massIntersect.PerimeterCurves();
perimeterPnts = Curve.PointAtParameter
(perimeterCrvs<1>,(0..0.3..#10));
perimeterNrmls = Surface.NormalAtPoint
(massIntersect,perimeterPnts)
.Reverse();
projectedPnts = Point.Project
(perimeterPnts, Plane.XY(), perimeterNrmls);
projectedLins = Line.ByStartPointEndPoint
(perimeterPnts,
List.Flatten(projectedPnts<1>,-1));
projectedSrfc = Surface.ByLoft(projectedLins);
polySrfc = PolySurface.ByJoinedSurfaces(
List.Flatten([massIntersect,projectedSrfc],-1));
GeometryColor.ByGeometryColor(polySrfc,
Color.ByARGB(255,225,185,145));
```
#### Conclusion
Once the initial massing and overall design direction have been established, computational tools can be further utilized to delve into the finer details of the design process. Here's how this iterative approach could unfold:
1\. Division into Functional Sub-volumes: Computational algorithms can be employed to divide the enclosed volumes into functional sub-volumes based on programmatic requirements and spatial relationships. This process takes into account factors such as room sizes, adjacency preferences, and circulation patterns.
2\. Analysis of Circulation, Lighting, and Ventilation: Computational simulations can be conducted to analyze circulation patterns within the space, ensuring efficient movement between rooms and areas. Lighting and ventilation analyses can also be performed to optimize natural light penetration and airflow distribution within the building, enhancing occupant comfort and energy efficiency.
3\. Creation of Openings and Apertures: Based on the results of the analysis, computational algorithms can generate openings such as doors, windows, and other apertures in strategic locations within the building envelope. These openings are placed to facilitate desirable views, maximize daylighting, and promote natural ventilation while maintaining the overall integrity of the design.
4\. Iterative Viewing Exercises: After creating openings and apertures, designers can conduct iterative viewing exercises from each aperture to assess the visual connections, sightlines, and framing of surrounding views. This process allows for refinement and optimization of the building's orientation and fenestration to capture desired vistas and enhance the overall spatial experience.
By employing computational tools throughout the design process, architects can iteratively refine their designs, optimize performance criteria, and create spaces that are not only functional and efficient but also responsive to their context and users' needs. This integrated approach fosters innovation and enables designers to explore new possibilities in architectural design.
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