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Reconstructing Palladio’s Villas: 1

Reconstructing Palladio’s Villas:

A Computational Analysis of Palladio's Villa Design andConstruction Process

By

Lawrence Sass, PhD

ACADIA Conference Proceedings, 2001




Abstract

This project is ongoing research focused on finding a method of reconstruction, using

computational devices to build, represent and evaluate Palladio's un-built villas in three-dimensions. The first of The Four Books of Architecture contains text and imagesexplaining Palladio's design and construction systems in the form of rules. These rules

were written for the masons and craftsmen of the 16th century, offering one and two-

dimensional data on each of Palladio's villas, palaces and churches. The text only offers a

general treatment of the villas; it is missing construction data and rules needed to executea full reconstruction of an un-built building.

Many have attempted to reconstruct Palladio’s work in drawings, wooden models andthrough the used of computational devices. This project presents a new method of

reconstruction through the definition of construction rules, in addition to shape and proportional rules defined by previous scholars. This study uses the Villla Trissino in

Meledo as a test case for the process. The end product is a presentation of a method for reconstruction in the form of a three-dimensional analysis of Palladio's design and

construction rules and a demonstration the new construction rules, found as a result of

this study. The goal is to recreate all of the villas with the same method and rules.

The work began four years ago as a pilot study focused on modeling Palladio's villas inthree-dimensions. The models resulted in a pictorial representations of the villas found in

the Four Books of Architecture. They were not constructed by the rules in Palladio’s text.

This current version of the project is focused on reconstructing all of the thirty villas in

detail by Palladio’s rules. This method required a complete rewriting of the rules from the Four Books of Architecture and a few additional rules from an analysis of the existing

buildings. The rules were applied to a simple floor plan and elevation drawing in order to

transfer Palladio's original sketch drawings in a CAD environment. The reconstructedsketches were used to create a three-dimensional CAD file by construction rules.

Afterward, three-dimensional prints, two dimensional drawings and renderings were

created from the model for evaluation. Final results of each study contain textural as wellas visual information on the reconstruction. The resulting villa model demonstrates how a

villa can be built from the rules in the Four Books of Architecture. It also demonstrates

qualitative and quantitative input and output from a computational device.




1.0 Introduction

This project is a follow up on two papers written by Wittkower and Stiny, on methods for

reconstructing Palladio’s villas by rules, shape and computation.1

This paper adds to the

theory by reconstructing the villas in three dimensions verses two, using computer

modeling and three-dimensional printing. This process requires information beyond the programmatic line representations presented by Wittkower and Stiny. It requires material

related to masonry, wood and stone construction in addition to the general design

materials found in the Four Books of Architecture. Within this paper I will demonstratethe process used to reconstruct 30 of Palladio’s villas in the form of computer modeling

(fig 1). Each resulting villa was represented using a variety of output devices such as

computer rendering, conventional plans, sections and elevations on paper and three-dimensional printing. This paper will also demonstrate that how Palladio’s text could be

applied to the reconstruction of an entire villa exclusively by rules, from the foundation

to the roof. Most important is that the rules used to reconstruct each villa have beenrewritten in a format that should allow for a direct application to a computer program or

shape grammar. This paper does not claim that Palladio’s rules will lead towards a

perfect reconstruction. Instead it is a discussion of a process of qualitatively and

quantitatively evaluation and design choice. This paper will demonstrate Palladio’sdesign rules, and a process of reconstruction starting from a two-dimensional

reconstruction, concluding with a three-dimensional representation and evaluation.

Fig.1 Process of sketch to cad to three-dimensional product representation (3d

Print)




Fi . 2 Palladio's ori inal drawin s




Fig. 3 Villa models: built in white, partially built or unbuilt in gray




2.0 Villa Design: The First Two Books of Architecture

From 1538 to 1570 Palladio designed over 30 villas throughout the Veneto of which

twenty-three are recorded in the form of drawings in the Four Books of Architecture.

Bertotti Scamozzi recorded the remaining six villas in the 18th

century in the form of

etchings. Most important is that Palladio wrote the rules and drawings for the Four Booksafter the villas were built. The drawings reflect what he wanted the buildings to be - not

the built condition. Of the thirty drawings only 19 were built and of those only two

resemble any of the drawings. Most of the built work differed dramatically from thedrawings found in the Four Books or in Scamozzi’s text.

2Some of the built works are

missing the barns, towers or porticos. Again the goal here is to reconstruct Palladio’s

ideal intentions (the drawings in the Four Books) and not the built conditions, by the rulesexpressed in Books One and Two. There are three facts relating to the drawings that

make reconstructing Palladio’s villas a challenge:

• Palladio created the drawings and text in the Four Books of Architecture after the buildings were built. So the drawings in the text are a representation of howPalladio wanted the villas to be and not a representation of the built condition.

• The drawings are in constant conflict with themselves, dimension strings do notadd up to over all sizes, and the drawings contain little information on the

buildings’ physical construction or how the rules were applied.

• Defining the rules, what are they, how do they work in construction and design.

What are the unit measurements that Palladio uses to define sizes of objects, andhow do these objects work by the rules in a space or spaces.

There are two types of villas within the corpus, the country villa or farm villa, and theurban villa. The country villas were composed of a main house and barns, set at the outer

ends of the site. The barns extended from the main house towards the front of the

property ending with a wall and a small opening aligned with the entry of the main house.Country villas were farms, whose income offset the costs associated with owning such an

expensive piece of property in the countryside. The area within the barns was used togrow expensive crops and care for livestock. Urban villas such as the Villas Foscari and

Rotunda were used for entertainment and as an escape from the hectic pace city life, theydid not have barns (fig. 4).




For both the county and urban villa, the main house contains three levels of service. The

main level or the one elevated from the street level known as the piano noble was used

for entertainment, and as sleeping quarters for the patron. The second floor contained

apartments for servants and storage space for grain. The lower level was used for cooking, storage and cleaning. Spaces were organized symmetrically around a hall, such

that all spaces on the right were the same as those on the left.3

Principle spaces (loggias,

halls, and courts) were seen as the most beautiful to be placed in full view upon entry.4

3.0 The Reconstruction Process

The goal is to reconstruct Palladio’s villa from the drawings in The Four Books of

Architecture and Scamozzi’s etchings by Palladian rule. This task requires far moreinformation than the two-dimensional reconstructions of Stiny/Mitchell and Wittkower.

The construction of walls, ceilings, roofs and basements require information not always

found, or clearly articulated in the Four Books of Architecture. That material is acquired

here through a constant survey of the built conditions and Palladian research. In additionto the construction material, the process must also contain methods for checking rule

application during the process and in the resulting model. In summary, the process

involves qualitative and quantitative methods for evaluating and testing the process andresulting model.

Fig. 4 Country villa (Pojana) and an urban villa (Foscari)




The process used here is done in a series of steps starting with a villa manual andconcluding with a three-dimensional representation known as a villa model . The villa

manual is a clarification of rules from the Four Books, by rewriting and illustrating each

rule in the form of a simple line of text. This manual contains all of the programming,

construction and ornamental rules needed to reconstruct a villa from a site plan. The firststep is to reconstruct the site plan of the villa and the barns, in form of a line drawing a

process similar to Palladio’s sketch representations not found in the Four Books (fig.5).The second step is to apply construction rules to the line representation of the plan in

order to create a digital representation of Palladio’s design intensions. The third step is to

reconstruct a digital representation of the elevation from the previous digital plan and theelevation drawing in the Four Books. Finally, three dimensional construction rules and

ornamental rules are applied to the plan and elevation drawings leading to a villa model

representing of half of the final villa (fig. 10). The villa model is used to create plans,

sections and elevation drawings for measurements in addition to a three dimensional printand renderings of complex spaces. Throughout the process each rule taken from the villa

manual, or rule invented by the author or others is recorded on a spreadsheet. (see:Appendix-A)

Fig. 5 Reconstructing the Villa Pojana plan in line form from the site and barn on the left

to the reconstruction of the final plan in line form on the right




3.1 Reconstructing the floor plan

This reconstruction system is a set of parametric shapes, systematically applied to the

plan diagram (fig. 5) once the proportions and general shape of the plan has been

constructed (fig. 6). The construction system is used to create a finished plan of walls,

ceilings, porticos and stairs. These shapes are plan views of construction items and newrules created by the author. New rules must be written to fill the gaps for general rules

written by Palladio. They are scalable, stretchable images representing design and

construction rule sets that are dependant on the completion of the previous set of objectson the plan for their parametric assignment. For example, villa wall thickness is defined

by the ceiling type assigned to the plan, if a room has a heavier ceiling then the walls

must be thicker. If a lighter ceiling type, such as wood joist are used they require athinner wall thickness. But door or window placement does not depend on wall thickness;

it is dependent on room adjacency and views to the outside world. So, wall thickness

cannot be assigned to the plan until the ceiling type is defined on the plan diagram. The process requires the assignment of nine steps each with a series of rules from the villa

manual that can be applied to the plan. The final representation is a quantitative

representation from Palladio’s plan drawing in the Four Books.

Plan Reconstruction Steps (fig.6)

1. Assignment of spaces

2. Ceilings notation

3. Wall thickness notation

4. Portico

5. Columns and arches

6. Stairs and stair pedestals

7. Door notation

8. Window notation

9. Detail notations




Fig. 6 Reconstruction of the Villa Cornaro plan drawing from a line




3.2 Reconstructing the Elevation

Palladio's elevations are pictorial representations of the plan, projecting and adding

elements from the piano noble. A closer look at the plan and elevations demonstrates that

two drawings don’t match. Lines are off or sometimes drawn differently from the plan all

together. The elevation design sketch is transformed to a digital representation in ninesteps, each focused on representing some aspect of the construction, such as wall height

variation and column location. Most are focused on a pictorial representation of the parts

by locating windows, doors, pediments, moldings and entablatures. Each step listed below for this system was taken from a survey of villa drawings in book two of the

Quattro Libri. Most steps in this section are symbolic notations that can be applied to the

initial wall shape. Most of shapes for the elevation reconstruction are fixedrepresentations or symbols used to locate the objects on the elevation. Finished sizes are

not of the highest concern here the goal is to create a pictorial reference for heights and

symbolic location.

Elevations Reconstruction Steps (fig. 7)

1. Initial Shape

2. Walls and Floors

3. Cornices

4. Portico Steps

5. Columns

6. Moldings

7. Doors and Windows

8. Roof and Pediment

9. Details




Fig. 7 Reconstruction of the Villa Cornaro elevation




3.3 Constructing the Villa Model

The Queen Anne Grammar 5

and the Frank Lloyd Wright Grammars6

use parametric

grammars used to specify shapes in the styles of the architects. The difficulty with the use

of these grammars here is that the origin of the sizes for the shapes is unclear. There is

little documentation defining the sizes of the objects and the reasoning behind their fitness requirements. To address the issue, this study has created a spreadsheet containing

variables missing from Palladio’s drawings.

There are twelve steps toward constructing the final villa model. Each step requires sizingand location information from the reconstructed plan and elevation drawings. Just as with

the Queen Anne grammar, a building part is assigned a set of variables also listed on the

spreadsheet from rule variables defined in the villa manual. The rule application

developed here is not formed from many pre made objects that are combined to make afinal product, but formed from procedures and profiles designed in the Palladian style.

Villa Construction model Steps (fig.8)

1. Initial plans

2. Walls

3. Ceilings

4. Cornice

5. Portico

6. Staircase

7. Columns

8. Moldings

9. Doors

10. Windows

11. Details

12. Roof




Fig. 8 Three steps within villa model reconstruction (Initial plan, walls, columns)




4.0 Villa Manual of Rules

The Four Books of Architecture breaks rules up by object, proportion and spatial

ordering. Text rule representation in the text and application to a reconstruction can be

confusing, the text was meant to be read by a 16th

century mason or architect. The villa

manual is broken into 16 sections based on vicenzentine brick, means of measuring,objects such as columns and mathematical rules such as ceiling height or window

opening sizes. Within each section of the manual is a rewriting of the rule from the Four

Books or a new rule needed to construct a detail or a space not mentioned in Palladio’stext. A typical series of rules from the villa manual are written in the following format:

RULES FOR STAIRS (fig. 9)

8.1.pa - Staircases may not obstruct other places, nor be obstructed by them7

8.2.1.pa - They should be hidden from those that enter the house8

8.2.2.pa - They should be in a place so that the most beautiful part of the house is seen first9

8.3.1.pa - Three openings are required in staircases10

The number on the right of the rules indicates the rules section, and rule division withinthat section. The “pa” refers to a rule written by Palladio. A rule labeled “ls” or “sm”

means that the rule was author by someone else. Within the text rule representation and

application can be confusing and hard to apply. In this study the manual of rules is based

on three rule types: plan programming rules, construction rules and ornamental rule.

Fig. 9 Rules for a stair construction. D = riser height & brick thickness, tr = tread

depth




4.1 Input - Plan Programming Rules

Plan programming rules are spatial, two-dimensional rules used to construct or

reconstruct any plan (with some degree of accuracy) by rule and proportion in line form.

These rules organize the plan from the site, to wall and stair layout. Two examples of

plan programming rules are those used to organize the loggias and internal spaces byPalladian rule. First, Palladio says that “the loggias, halls, courts and magnificent rooms

as principal spaces.”11

Second, that these principle spaces should be seen first (halls) and

the secondary spaces should be hidden from view (stairs, kitchens, servant areas).12

Based on these rules a villa will never have a grand internal staircase at the entry. There

are 15 plan programming rules taken from the original text that can be used to

reconstruct most villa plans. I also added eight additional rules simplifying and filling inmissing gaps from the text. For example the floor plans found in the text confuse the

issue of room size, some historians say that the dimensions listed on Palladio’s floor

plans refer to dimensions from face of wall to face of wall. Unfortunately Palladio’sdrawings vary in representation. When the dimensions are added to define the plan sizes

they never amount to a consistent rule based on measurements from face of wall to face

of wall, or center of wall to center of wall. The rule here defines room sizes from center

of wall to center of wall, adding wall thickness later. The final floor plan and barn plan isrepresented by a series of line similar to Wittkower’s study. In summary plan

programming rules organize the floor plan by Palladian rule from the site to the stairs in

line form (fig. 5).

The order of application begins with site rules followed by loggia rules, and last are

spatial rules used for room layout and ceiling height proportions, starting with principle

spaces. For example, site rules used to reconstruct the a villa say; “the house should be

placed in a convenient location in the middle of the site.”13 Second “the barns may not bean impediment to any other part of the main house”, thus they are placed at the perimeter

of the site. Third, the steward and bailiff should be placed near the outer gate for safety,creating dovecotes and a large fence at the villas entrance completing the barn assembly

(fig 5).14

Rules for the main house also follow the plan programming process by placing

the loggia at the front of the villa. The first space entered is a magnificent barrel vaultedhall, and the stairs are out of view, while the nicest rooms are at the front of the villa, the

smaller lesser rooms are towards the back. The final plan (fig.5) is a line representation

based on dimensions from the original drawing, prepared for construction details andinformation.




4.2 Input - Construction Rules

The second set of rules are construction rules applied to the line drawing to create a

functional floor plan followed by an elevation drawing from which three dimensional

villa model can be constructed. The construction rules are applied the floor plan line

drawings to define wall thickness, stair sizes, and true window and door locations (fig 6).Construction rules are also used to create the elevation, accurately. Rules are given by

Palladio to define the outer shell of the elevation drawing (fig. 7 - 1-boundaries).

Construction rules are used to define the cornice, column types and roof slope. The finalrepresentation in the plan and elevation is a representation of the drawing from the Four

Books, each reconstruction in nine steps. Most important is that the digital representation

demonstrates conflicts in the relationship of the plan to the elevation. For example the bumped out areas of the plan are not represented in the elevation. Columns may be too

thick to allow a person to pass through the portico comfortably in elevation, when they fit

perfectly in the plan. These two dimensional conflicts are resolved within the threedimensional reconstruction.

4.3 Input - Ornamental Rules

The final rule type in the villa manual are ornamental rules applied to complex areas or

surfaces in order to cover imperfections in construction, or to set a particular design

feature apart from another (window moldings, column capitols, etc.). There are somerules written for the construction of an ornament in the Four Books such as doorframes,

window moldings and column moldings, but there are few rules that state the conditions

under which they should be applied.

5.0 Output - Representation

The case studies are a presentation using four methods of representation and evaluation,

each method addressing both qualitative and quantitative issues.15

These representationalmethods address Schon's points on action-in-reflection in that this process is one of

learning by doing.16

Here the four methods include rule graphs, also known as

spreadsheets, used record object variables and rule equations, 3D printing of the modelfile followed (fig. 11) by 2D documentation and finally rendering used to visualize areas

of spatial conflict. The concept of representation is that the more opportunities offered to

visualize the design, the better the design results. Filmmakers and artists follow a similar

process by changing the viewer's position in relation to the artificial world with devices

from stereoscopic glasses to virtual reality. Their mission is to visually engage the viewer in the subject matter by changing the viewer’s point in relationship to the object being

viewed.17

In this study, rendering and model making tools as output materials from a




CAD file are used to create different architectural perspectives from a variety outputmaterials.

5.1 Output - One-Dimensional Representation

One-dimensional output refers to the graph presentation (spreadsheet) of text rules used

to build each villa model (found in the appendixes of the previous two chapters). They

are accompanied by graphic descriptions, but are not meant to serve as a substitute for thegeometric material.

18Each graph contains the rule, the element upon which the rule is

applied and a reference number for pointing to the rules definition. The rules in the graph

serve as text functions used to determined shapes from room size to column depth or mathematical formulas used to determine window heights, room heights or Principal door

sizes. This method of presenting textural rules along with the graphic representation is

similar to a method used to describe shape grammars where the element is described

along side its function.19

Text representation in this study will be used as a quantitative

means for evaluating the villa models.

Fig. 10 Cad representation of the completed Villa Cornaro vila model




5.2 Output- Two-Dimensional Representation

Two-dimensional output refers to conventional drawing - plans, sections and elevations,

used as comparative tools for evaluating the villa model against other drawings, such

those of Bertotti Scamozzi. Plans are cut four feet above the finished floor. Sections are

taken at the mid-point of both axes and elevations are taken at the extent of the propertylines. A bar scale and a north arrow accompany each drawing when necessary. These

drawings are a quantitative means of representing the villa model.

5.3 Three-Dimensional Representation

Three-dimensional output refers to physical model output from machines in the form of plastic or cornstarch. Three-dimensional printing or Fuse Deposition Modeling (FDM)

stands as the moment of truth in CAD modeling and detail. Mistakes created by

miscalculations in the creation of the CAD file, reveal themselves once printed in three

dimensions. The output process is similar to conventional printing with the exception of the material and the output platform. The villa model or CAD file is cut into many plan-

sections at intervals of 1/100 of an inch per section. Each plan-section represents one

print file. Each plan-section file is sent to the printer one layer at a time and printed uponthe previous layer. The final output is in the form of a plastic or cornstarch three-

dimensional object. The final model has a maximum size of 10" x 10" x 10" per part.

Large models are printed in pieces and glued together. Because the villa can be printed atany scale it stands as both a qualitative and quantitative means of representation (fig.11).

5.4 Renderings

Renderings are used to simulate various design conditions such as lighting, surfacetextures and form while placing the viewer inside of the space. Rendering output here isfocused on design issues and not on representing the full building. In most cases, the

issue is about the lighting conditions of a space or the formal qualities of an outdoor space, such as a loggia. Each study uses geometric models of a particular space, the only

areas modeled are those in relation with the issue. Renderings are used here to

qualitatively evaluate interior spaces and some exterior forms.

The rendering process uses radiosity models, whose surfaces are texture mapped andraytraced. In order to save on computer processing time, the full CAD file is copied, and

areas not within the view of the rendering camera are erased from the file. The goal is tocreate a stage set of geometric surfaces from the villa model, upon which textures can beapplied. The process starts with a solid geometry file, which is translated to a facial




representation. All solid information is removed model to be rendered. In other words theonly geometry translated from the CAD representation to the radiosity program contains

the geometry of the space and adjacent spaces within the frame of the camera.

Texture maps (taken from photos of existing villas) are used to create surfaces similar to

those in the built conditions. These maps allow the viewer to evaluate rendered images onthat architect's terms. This means the walls appear to be the walls that were built by that

architect. High-resolution texture maps are applied to each geometric surface within the

frame of the camera. When rendering ideal day lighting conditions are needed to definesurface texture, color and smoothness. The goal is to infuse the model or space with just

enough light so as not to over or under illuminate a surface, which creates dark patches in

detailed areas. The lighting goal is to offer just enough to create a contrast in surfaces.

The final step is to raytrace the radiosity model and texture mapped surfaces, resulting ina high-resolution image

Fig. 11 3Dprinting techniques used to view models in physical form. Smallest

model is a sketch representation with very little detail, largest model is a detailed

representation




6.0 Case study a: reconstructing The Villa Trissino, Meledo

This chapter is a presentation of four attempts to reconstruct the un-built villa Trissino in

Meledo (fig. 12) reflecting how the villa would have been built using the rules in the villa

manual. The three previous reconstruction attempts were evaluated in rendering or 3D

print form only. Each result from the studies differed slightly based on differentinterpretations of the rules by different people. The first attempt, was part of the simple

representations constructed for a CD-Rom project (fig 3). The villa model had no

interiors or detail such as column or cornice moldings. The second reconstruction wasundertaken in a workshop the following year. Students reconstructed parts of the villa,

later combining those parts to create a full villa model. The final results were composed

of interior and exterior renderings and a three-dimensional printed model. There were noattempts to record decisions or a documentation of the final model. The third version,

completed by Isaac Persley an undergraduate architectural student, was a research project

focused on building by the rules and recording the steps in graphic and textural form. Therules used in this study were recorded on a spreadsheet along with a drawing file defining

the application of the rule visually in the form of step-by-step pictorial documentation. It

was also printed three-dimensionally. The fourth and final version was created using

methods defined in this paper. There are one, two and three-dimensional records of alldecisions used to reconstruct the villa model as well as a three-dimensional print and

renderings of the central space.

Fig. 12 Palladio's plan of the villa Trissino in Meledo




The existing site for the Villa Trissino contains two dovecotes and parts of the lower barns and a stone fence. It has been debated whether the designs of the barns are

Palladio's, or that of a lesser architect.20

History has it that the villa was never constructed

and that Palladio never designed the existing dovecotes. As described by Palladio, the

main house sits atop a beautiful hill over looking farms and small waterways.21 The villaitself is similar in design as that of the Rotunda, a suburban villa with a circular hall and

adjacent hall spaces. The Villa Trissino in Meledo combines a sense of dramatic theater like that of the Villa Rotunda, with the workings of a true farm like that of the Villa

Pojana Maggore22

Staying true to his rules, Palladio places the villa atop the highest

point on the site from which barns cascade down and around to it’s outer ends.

To start, the reconstruction an initial grid (a & b) for the main house was placed atop thehill along with a barn grid at a lower point. These grids are used to define the spacing of

the walls and columns. The measurements for the villa plan where taken from Palladio's

drawing (fig. 13), while the barn grid was an interpretation of the dimensions (fig. 14)from the drawing-there are no measured drawings of any kind for this building. The barns

are divided into two sections, one circular and the other half square. There are two

methods that could be used to find the center point of the circular barns. The first methodis to add the distance between the columns and the diameter of the column defining the

barn circumference.

Fig. 13 Site plan of the Villa

Trissino with grid-a and grid-bFig. 14 Grids-a and grid-b




The second is to measure the distance from the edge of the steps leading to the lower terrace to the first column in the circular barn. The length of the barn is found by adding

the columns and their diameters. I had to refer to Bertotti Scamozzi's drawing for the

number of columns and the spacing between the columns to define the length of the

barns. The villa barns also sit alongside of a thin waterway, specified in Palladio'sdescription of the villa.

23

6.1 The Reconstruction

One fundamental problem with the Palladio's drawing is that one of the side rooms ismissing a dimension note needed to define the width of the room space and the adjacent

run of the stairs. Palladio provides the length (30ft.) but not the width. This dimension

defines the overall size of the space, and it helps to define the shape and ordering of the

stair. It is possible that the width of the space could be a ratio such as 2:1 (15'), or 3:5 thatwould make the missing dimension 18'. Both numbers are too small to create the adjacent

flight of stairs that would clear the doors below. The proposal here calls for the space to be 22' wide, which should clear the door if there is a winding stair (fig. 15).

Fig. 15 Two solutions for the missing dimension. Scheme (A) offers a good ratiofor the space 2:1 but there is not enough space in the stair to clear the 6'6" door.

Scheme (B) offers space for door clearance but the number does not fit with

Palladio's proportioning system. Any number greater than 22' dramatically breaks

Palladio's rule for the maximum length of a stairs run (Palladio, A., p. 34).




6.1.1 Plan Reconstruction

The plan was reconstructed from the dimensions listed on Palladio's drawing and the

conjecture defined above (fig. 15). Once the basic layout for the wall grid along with

dimensions was established (fig.14), and the process of adding reconstruction begins (fig.

16). The only area of conflict within the plan reconstruction was in the connection between the house and the circular barn. It is unclear how the two were connected in the

Palladio’s drawings. In this solution, the attempt was made to join the barns to the outer

wall of the main house.

6.1.2 Elevation Reconstruction

The elevation did present some problems in height definition, which varies a lot between

the two barns and the main house. In addition to the variation in heights of the barns, the

dome became as much of a construction issue as was a design issue. The dome is drawn

in the Quattro Libri with a straight line at its base, where the roof of the villa meets thedome, similar to the drawing of the Rotunda. There are no rules for the height of the

dome, nor rules for its construction. Here again, another conjecture is made to define the

height of the dome. In this case the guess is set at 72' to the top of the dome, the samedimension as the inside radius of the barns (fig. 17).

6.1.3 Model Construction

Model construction is broken into 12 parts as mentioned earlier. Here the main conflict

expected to be resolved in the modeling process is the construction of the large domeover the central space. Additional areas are the stair construction, basements, junction

between barns and the house and the roof of the main house.

6.1.3.1 Initial Plans

Although the first level of the plan shows the barns and the basement as one piece, the

site separates the villa and its into three separate pieces: the basement, the upper barn and

the lower barn. The walls at the basement of the villa follow the rules system for walls,which states that they are to be twice the thickness of the walls at the piano noble.

However, the upper story walls do not follow Palladio's rules tha call for them to be half

a brick thinner than the piano noble. Since the outer wall is flush and without moldings at

the second level, I constructed them at the same thickness as the piano noble (fig. 18).




Fig. 16 Plan reconstruction derivation




Fig. 17 Elevation reconstruction derivation




6.1.3.2 Walls

The floor-to-floor height is missing from the original Palladian drawing for the piano

noble and the barns. However he does give dimensions for the height of the walls fromthe piano noble to the bottom of the roof cornice. Here 17' was given to the first floor,

one to the floor thickness and 8'-0" was given to the upper story. In this case the

conjecture for the basement wall height was taken from previous studies defining the basement at 11'-0" in height. The barns were given heights of 15' for the lower barn and

15' for the upper.

Fig. 19 Wall derivation

Fig. 18 Plan Reconstruction using wall notations from the plan reconstruction




6.1.3.3 Ceilings, vaults and floors

The only ornate ceiling in the villa is perhaps a barrel vault at the entry hall. It turns out

that there are two rooms with the possibility of supporting a vaulted ceiling the entry

room and the small outer room, adjacent the connection to the barns. The middle space is

a double height space similar to a large palace space with a flat ceiling. Basement vaultsare semi elliptical vaults (fig. 20).

6.1.3.4 Cornice

The cornice is the most complicated part of the assembly. Each cornice type (c1, c2, etc.)

is composed of three design conditions - an extrusion of the profile, a cap condition at the

corners where two cornices meet and a reverse cap condition where two cornices meet ina corner. Composed of two parts, the Corinthian order is customized in four different

ways. The first of the Corinthian orders is used for the balcony projection under the

portico (c2); the second is used at the rotunda (c3), the third is the most ornate (c4), inthis case placed under the pediment; the last is a flattened version with the least

ornamentation, and it is used under the roof (c5). The most complicated connection or joint is at the portico. Here Palladio extends the ornate entablature (c4) over the columns

away from the flattened cornice (c5) that surrounds the walls.

Fig. 20 Ceiling derivation




6.1.3.5 Portico and steps

There are three different portico stairs, each with its own function and layout. Types (s1)

and (s2) are formal types leading to the porticos of the villa. Types (s3) and (s5) are

service stairs leading to the upper and or lower barns. Type (s5) is a formal stair dividing

the two gardens. The greatest conflict is in (s5) which is modeled differently thanPalladio's original drawing. Palladio's drawings showed a set of stairs heading into the

lower barns. This gave little room for a landing. The solution here calls for a switch back

stair leading to the lower barn. The negative part of this is that it is uncovered.

Fig. 21 Cornice types, refer to fig. for profiles

Fig. 21 Porticos and exterior stairs




6.1.3.6 Staircases

There are three types of stairs, each made of the standard brick supporting system, but

there is question as to how the formal stair might have been constructed. Palladio shows

the stair as a wrapping rectangular stair without an inner wall. It is not clear how it would

support itself with out a wall so one was added in this study. The problem is that there islittle room for the door and passageway shown in Palladio’s woodcut.

6.1.3.7 Columns and arches

It is unclear as to what orders Palladio might have used for the barns, and the main villa.

Palladio specifies that the loggias are to be of the Corinthian order and that the barns are

Tuscan. Bertotti Scamozzi challenges this by saying that the upper barns were designed by Palladio to be of the Ionic order and that the lower barns were meant to be of the

Tuscan. It is most likely that the real challenge of the orders is in the dome. Palladio does

not assign an order to the half columns in the dome. In the Four Books he says "There are some half columns in the hall, that support a gallery, into which one goes from the rooms

above; which by reason they are but seven feet high, serve for mezzati.24

" BertottiScamozzi lists the order under the dome to be Corinthian. I have also listed the order to

be Corinthian in the documentation, but this will be challenged in the visualization.

Fig. 22 Interior stairs




6.1.3.8 Moldings

There are two molding types (double and single) surrounding the lower levels of the villa

and barn.

Fig. 23 Columns and arches

Fig. 24 Molding Reconstruction




8.1.2.9 Doors

Room doors worked fine when installed by Palladio's rules. The formula for the principledoors did not work at the second story. The height of the opening and archway at the

colonnade had to be altered to compensate for the large entablature.

8.1.2.10 Windows

The generic window size formulated for the villa was also used in the upper and lower

barns.

Fig. 25 Doors

Fig. 25 Windows




6.1.3.11 Details

Here, two principal door types are used, the scroll being the most formal of the two.

Balustrades and newel post are used at the balcony level.

6.1.3.12 Roof and pediment

The pediment is of the Corinthian type angled at 23.2 degrees, supported by minor and

major types.

Fig. 26 Details

Fig. 27 Cornice, roof truss and roof




6.4 Results and Conflicts

As with any reconstruction or design problem, there are major and minor conflicts and

contradictions that are cause for design invention, in this study there were two. First,

there are no rules for defining the height of the dome. Although the villa Rotunda is

rendered with a similar dome, the two cannot be compared in construction or design. TheRotunda's dome is drawn almost as if it were metal with little wall space between the

base of the dome and the top of the villa roof. The Trissino dome has walls extended far

above the roofline for the main house and the dome has a radius lower than that of theRotunda. Palladio’s drawing shows the Villa Trissino dome with moldings and details

around the upper portion of the dome, which could mean that the dome was composed of

brick not metal. The second conflict is over the half columns in the central space.Palladio does not specify an order. Scamozzi speculates that the columns are of the

Corinthian order while Burns defines the order to be Ionic. The two possible orders are

tested in this next section.

Fig. 28 Three-dimensional print from the cad-model




6.5 Interior Studies

The question here is what was the order of the half columns? The possibilities include the

Ionic and the Corinthian orders as mentioned by Scamozzi and Burns. There are two

references that can be taken from other dome spaces similar in composition to this villa.

The first is the Tempietto Barbaro at Maser, which happens to also have a portico of theCorinthian order and a domed space articulated with half columns also in the Corinthian

order. These half columns support a balcony of thin balustrades, above with no

supporting newel post. The second space is similar to the design of the Villa Rotunda,which is of the Ionic order on the outside and frescos with columns of no particular order

on the inside. The inner wall below supports the balcony, lined with balustrades and

newel posts but not columns. Here the two are tested qualitatively.

Fig. 29 Proposals for the Corinthian and Ionic orders at the dome




Fig. 31 Rendering of the central hall with half columns in the Corinthian Order




6.6 Summary of Findings from the Villa Trissino

The Villa Trissino is a palatial villa of a massive order, set atop a hill, along side a

beautiful creek, assembled by rule with few conflicts. Here the conflicts were resolved by

referring to churches or villas of similar design and construction or resolved through a

closer examination of the physical construction (fig. 15). In spite of the amount of thenumber of issues inspired by each study, each attempt to reconstruct a villa reveals

unexplored information leading to new questions and new rules. The Villa Trissino

presented a process and a product more than a particular design finding. The lessonlearned from this study was that rule conflicts lead to the invention of new rules (design)

or the rewriting of the existing. Based on information from the past set of reconstructed

villas (fig. 3) there are fore seen studies that will render many design conflicts.

7.0 Towards a new Palladian Grammar – Reconstructing the Villas

As with most computational projects, two areas of learning are at play between thecomputation and the architect. Here, two lessons were learned about Palladio’s design

process and construction process. First is that Palladio's plan sketches are spatial

representations from which construction rules can be applied. In other words, design rulesare represented in the form of lines drawings, while construction rules are noted by text

and graphics. Second, there are many conflicts and contradictions in the drawings,

particularly in detailed areas. The drawings were never meant for construction, they aremeant to serve as simple representations of the villas. The first thing that must happen is

to convert the plan and elevation to a digital accurate representation before any three

dimensional rules can be performed. Third lesson is that the rules actually work ingeneral terms. Wittkower and Stiny/Mitchell were right. Most rules were very general

mostly allowing operations on general areas of villa design and construction. Additionalrules such as wall thickness, ceiling thickness rules, or roof rafter rules were used to fillrule gaps.

There were also lessons learned about the reconstruction process as well. First, is the

issue of evaluation and that resulting materials should be presented and evaluated under qualitative and quantitative terms, meaning that the material must be measurable in scale

and quantity. Architects design spatial material which is best viewed in three-dimensions

either through rendering or after construction in the form of a simulated model. Last,there is always more than one solution to any design problem. Single solutions can limit

the level of understanding for a particular issue. Multiple variations of one theme help the

evaluation process by expanding the questions through multiple representations of thesame idea.




As simple as it sounds fitness served as a major conflict in the execution of the rules.Conflicts were the projects greatest asset, they lead to design investigation or invention.

In fact it is how Palladio designed, by sticking to most rules while breaking lesser rules,

forcing him to invent new design solution to classical design solve problems. Design

occurs at the junction of conflicting rules. Unfortunately computational rules are muchmore rigid, containing many fitness requirements. Little has been written on the issue of

fitness and rule, also referred as a constraint model.25

If the process of reconstructionwere a linear rule operation, starting with the site and ending with a pyramid style roof

set atop villa walls, each rule will define a new object that must be aligned precisely with

the previous component. As the model is constructed the program would be able tocalculate each component and adjust the size or insertion for each component

automatically through fitness extensions to each rule. Fitness challenges the extent of the

rule by requiring a certain amount of flexibility in the execution of a rule. But if the rule

is too flexible is cannot be defined as a rule of a certain category or type. The challengeand creativity is in writing the rule not in its execution. In this study fitness pertains to

two or more objects that come in contact with other objects, requiring that one or moreobjects fit inside, next to, along side of or between two or more objects.

26A good

example of fitness is the case of the roof rafter rule. (fig.27) The rules require rafters

between roof joist every two feet depending on structural loads. Each rafter section is

made of three to four smaller members bearing loads on each other (not shown in fig. 27).The farther from the corner the more members a section will contain. In addition the

angles of each member must support the vertical forces of the roof, and the rafters must

be placed 6' to 8' apart. Here the rule or fitness requirement used to build one rafter did

not work for another. Each rafter was of it’s own construction. The question here is howto break down rule conditions based on fitness and degrees of fitness.

In conclusion this paper is a presentation of an un-built villa in many dimensions built byPalladio’s rules. These rules will also be used to create 29 other villas at the same level of

detail. This project demonstrated that a computational process operates with two types of

rules, construction and design. Construction rules are predominately parametricinstruments used to construct objects once origin points have been defined. At both the

level of construction or design, real design decisions happen when rules conflict. The

question is do we create more rules to manage constraints within other rules, or is there a process of invention based on design constraints that may lead to a better understanding

of the design machine.




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Notes

1 Stiny/Mitchell 1978 p. 6

2 Scamozzi, B., 19763 Palladio, A. 1965 Book I, Chapter 21 par. 1

4 Palladio, A. 1965 Book II, Chapter 2 par. 1

5 Flemming, U. 1987

6 Koning, H., 1981

7 Ibid., Book I, Chap 28, par 1

8 Ibid., par 2

9 Ibid.

10 Ibid.

11 Ibid,

12 Ibid,

13 Ibid, Chapter 13, par. 1

14 Ibid, par. 5

15 Tufte, E R, 1997

16 Schon 1987

17 Crary, J. 1990 p.39

18 Mitchell, W J., pp. 137-153

19 Stiny, G. 1981

20 Puppi, L. 1973, pp.384-385

21 Palladio, A., 1965 p.51

22 Ackerman, J, 1966, p.73

23 Palladio, A. 1965 p.54

24 Palladio, A., 1965, p. 51

25 Gross, M 1987

26 Ibid., p. 95

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