Villa Capra "La Rotonda"
Introduction
Villa La Rotonda is a Renaissance villa just outside Vicenza, northern Italy, designed by Andrea Palladio.
The proper name is Villa Almerico Capra, but it is also known as La Rotonda, Villa Rotonda, Villa Capra
and Villa Almerico. The name "Capra" derives from the Capra brothers, who completed the building after it
was ceded to them in 1591. Like other works by Palladio in Vicenza and the surrounding area, the building is
conserved as part of the World Heritage Site "City of Vicenza and the Palladian Villas of the Veneto".
Building began in 1567. Palladio, and the owner, Paolo
Almerico, were not to see the completion of the villa. Palladio
died in 1580 and a second architect, Vincenzo Scamozzi, was
employed by the new owners to oversee the completion. One of
the major changes he made to the original plan was to modify the two-storey centre hall.
Project's Structure
The project is divided in three different macro-blocks, each divided in sub-blocks and so on. Each block has a function who generates it. The main function invokes the function of the three macro-blocks, wich invoke the function of their sub-blocks and so on. This structure divides the responsibilities of each function, making it easy to debug and modify. Each block is built in local coordinates and then positioned with appropriate rototranslations.
1 Facade
The ville is composed by four identical facades, so here is exposed the
building of one of them. At the end, the facade is replicated on all four
sides by the functions T and R.
1.1 Steps
The steps were made with the STRUCT function applied on a CUBOID and a translation (T) on the
coordinates y and z. SIMPLEX_GRID was used for the small walls on steps sides and a couple of
replicated CYLINDRICAL_SURFACE (one horizontal and one vertical) for the grate of the small windows
1.2 Tunnel
In the building of the tunnel behind the steps was used the function SIMPLEX_GRID for the simple polygons (the simple walls). The archway is made by two bidimensional NUBS for the archs and a product between them by the BEZIER (S1) function.
1.3 Colonnade
This part of the ville is composed by the columns and the two archways on the sides; them are both composed by different parts, so they're going to be analyzed singly.
1.3.1 Columns
The columns consist in a unique column, of whose composition is explained below, translated on x- coordinate.
1.3.1.1 Base and body
The column's base was made using a CUBOID and a surface above it generated by a ROTATIONAL_SURFACE used on a bidimensional NUBS. The body is a ROTATIONAL_SURFACE on a
NUBS too: the profile was made using the "6/5 at 1/3" rule, that says that the column's radius, at 1/3 of the height, is 6/5 of the base's radius.
1.3.1.2 Capital
It may appear not perfectly roundish, cause all domains have to be mantained low, in order not to load the entire project too much.
The capital,in ionic style, was made by a couple of bidimensional NUBS for the profile, and a series of BEZIER between them to generate the volute's lateral surfaces and relief. It was also used a TORUS_SURFACE to made the echinus between the volutes.
1.3.2 Lateral archways
The archway's base was made using SIMPLEX_GRID. The arch's pillars were made by SIMPLEX_GRID too. The arch is modeled by two bidimensional NUBS and a BEZIER between them to generate the surface, the same tecnique used for the tunnel.
There's a particular ornament in the middle of the arch: it has a particular shape, modeled using a SIMPLICIAL_COMPLEX with 8 vertices and 6 faces. All parts of the structure are put together in a STRUCT, after replicated on the other side of the colonnade.
1.4 Gable
This is probably the most difficult part to model, because it has a lot of details, such as the cornice or the drops. The other ornaments on the gable's background will be analyzed at the last paragraph ("Other Ornaments"), cause they were added at the end of the project along with statues.
For the cornices were used a series of bidimensional NUBS to make the profiles and then a BEZIER function on them to generate the surfaces, four in all, three for the triangle's boundary and one for the cornice under it. One point of each the NUBS that generate the triangle's boundary surface, were also used to make the gable's background: they were the vertixes of a triangle generated with a SIMPLICIAL_COMPLEX (three vertixes, one faces). The roof was also made using the points of the NUBS curves: it is a BEZIER on two NUBS, one generated using the point at the start of the cornice and the point at the end, the other one generated by a translation on z-coordinates of the first.
The drops were using the same tecnique used for the steps: a small cuboid a T (translation) function put into a STRUCT n times (with REPLICA function); the translation for the drops at the bottom is only on the x-coordinate, instead for those in diagonally the translation in on x,y coordinates. For the drops at the sides was used finally a translation on z-coordinate.
Every part described is put into a STRUCT after a series of rototranslation and scaling, in order to form the model Facade.
2 Wall
This part of the model includes walls, ornaments, windows and the principal door. The Wallmodel is then replicated, after appropriate rototranslation, on the four sides similarly to the Facades.
2.1 Wall
The simple walls were made using only SIMPLEX_GRID. Given height,width and thickness the wall is automatically generated, with holes in correspondence of windows and the door. For the ornaments were used the usual tecnique of two bidimensional NUBS for the profile and a BEZIER between them for the surface.
2.2 Small and Medium Windows
These windows were made by a series of SIMPLEX_GRID, to draw the frames and the glasses. These windows are generated automatically given the width and the height. The difference between medium and small windows is only that the second one has a grid, drawn by a series of POLYLINE functions; therefore, every model's window is generated using appropriate height and width and a series of rototranslation in order to put it in the right position.
2.3 Big Window
The frames and the glasses of the Big Window were made the same way as previous. It includes also some ornaments: the small gable at the top is a scaled clone of the facade's gable; the other ornaments were made using bidimensional NUBS for the profiles and the function CYLINDRICAL_SURFACE to generate the relative surfaces.
2.4 Door
The tecnique is the same used for the windows: the ornaments (the small gable also) are the same of the Big Window. The grid was made by POLYLINE functions.
2.5 Grate
The grate is simply composed by three horizontal and three vertical CYL_SURFACEs, as the grate of the facade's steps.
3 Roof
The roof is composed by two parts, roof and dome. It is generated and put in the right position with a series of rototranslation.
3.1 Roof
It was made using two 1-dimensional NUBS: one of them is a square, generated using the vertixes of the ornaments at the top of the wall; the other one is a simple point, put at the choosen heigth: a BEZIER on these two NUBS generates easily the roof.
3.2 Dome
The dome was a little difficult: it could be made by a unique NUBS for the profile and the function ROTATIONAL_SURFACE; but in this way we would have a unique model and would not be possible to color in a different way the various parts. Therefore was used a different NUBS and a ROTATIONAL_SURFACE for each part, in order to color it with the right color. Every part is after put into the STRUCT Dome, positioned on the roof with a series of rototranslation.
4 Other Ornaments
These ornaments are treated separatley cause they were made at the end of the entire project. The statues and the bas-relief are not the actual of Villa Capra, cause were not available the profiles of them. I used other statues, of wich I had the profiles.
4.1 Gable's Ornaments
The two simple ornaments at the sides are two TORUS_SURFACE scaled a little on x-coordinate. The plate at the center is a surface made by two bidimensional NUBS and a BEZIER on them. The bas-relief on the plate is the same statue described below ("Statue #2").
4.2 Statues
4.2.1 Statue #1
This statue in made by a series of pieces of surfaces generated with a NUBS and a CONICAL_SURFACE on it with the vertex on the same plane. Could not have used a unique surfaces cause the profile isn't convex, then it was necessary to decompose it in several different convex sub-parts. This statue is put in the right place with appropriate rototranslations.
4.2.2 Statue #2
This statue is more simple than the previous: its profile is almost convex, so could be used a unique profile (NUBS) and a CONICAL_SURFACE with the vertex on the same plane. This statue is also used for the bas-relief on gable's background.
Finally, as already said above, Facade and Wall structure are replicated with appropriate rototranslations, and the complete roof is put on the building. The entire structure is on a garden, modeled in a simple manner.
