a declarative design method for 3d scene sketch modeling

EUROGRAPHICS '93 / R. J. Hubbold and R. Juan (Guest Editors), Blackwell Publishers © Eurographics Association, 1993

Volume 12, (1993), number 3

A Declarative Design Method for 3D Scene Sketch Modeling

Stéphane Donikian Gérard Hégron

IRISA Campus de Beaulieu

35042 Rennes Cedex, FRANCE

Ecole des Mines de Nantes 3 rue Marcel Sembat

44049 Nantes cedex 04, FRANCE [email protected] [email protected]

Abstract

In this paper, we present a dynamic model associated with an intelligent CAD system aiming at the modeling of an architectural scene sketch. Our design methodology has been developed to simulate the process of a user who tries to give a description of a scene from a set of mental images. The scene creation is based on a script which describes the environment from the point of view of an observer who moves across the scene. The system is based on a declarative method viewed as a stepwise refinement process. For the scene representation, a qualitative model is used to describe the objects in terms of attributes, functions, methods and components. The links between objects and their components are expressed by a hierarchical structure, and a description of spatial configurations is given by using locative relations. The set of solutions consistent with the description is usually infinite. So, either one scene consistent with this description is calculated and visualized, or reasons of inconsistency are notified to the user. The resolution process consists of two steps: firstly a logical inference checks the consistency of the topological description, and secondly an optimization algorithm deals with the global description and provides a solution. Two examples illustrate our design methodology and the calculation of a scene model.

Keywords: Declarative Method, Intelligent CAD, Object Oriented Graphics, Knowledge Represen- t a t ion.

1 Introduction

In the current literature, several approaches have been attempted to design CAD systems. A first approach consists of an extension of classical CAD systems by using parametric objects or variational geometry [1], but models required by those systems are still very close to the traditional geometrical models and imply a bottom up design methodology by using imperative methods. Furthermore, this approach is not suitable when the design scene is complex or when the designer thinks about his project in a more semantical way. A second approach consists in building expert systems; these systems tend to focus on a particular domain and are only useful for routine design in a well known application domain completely formalized by a set of rules and constraints [2, 3]. Both approaches are far from architect's considerations during the first stage of design which is more a top down approach and a stepwise refinement process. A third approach met a constantly increasing interest in all CAD domains [4, 5, 6, 7, 8, 9]. This approach is more declarative and offers to the designer a more progressive and dynamic scene specification, leaving to the system the care of suggesting solutions, detecting inconsistencies and manipulating incomplete knowledge. An important difference between declarative and imperative meth ods (figure 1) is that a declarat ive method does not provide a unique solution like an imperative method does, but provides a model corresponding to a large number of scenes for which the system proposes one or more solutions.

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Figure 1: Declarative and imperative methods

The system presented in this paper, based on the third approach, offers to the designer the ability to describe the scene topology and geometry in a declarative way by means of properties and constraints on objects and their spatial configuration. The system deals with under-constrained and over-constrained scene descriptions and proposes to the designer one of the numerous scenes whenever the description is consistent, or explicits the inconsistency reasons. The goal of this paper is to show a complete view of our system, but to keep the paper reasonably short, some parts are not completely detailed but are referred to previous papers. The next section gives an overview of the structure of our system. Sections three, four and five describe the three different kinds of knowledge manipulated by the system. Section six deals with the two steps of the resolution process and section seven gives some details about the different kinds of inconsistencies which may occur during the design process. Finally some implementation details and illustrations of our method are given.

2 System Overview

We intend to apply the declarative methodology to architectural design. Our goal is not to get the final and precise geometric model of each component of the scene but to assist the designer in creating sketches meeting the main properties and constraints of mental images. The architectural project design we will try to simulate is based on a script which describes the scene from a user’s point of view who moves across the scene [10]. From each viewpoint, the user increases the scene description by adding new objects and new properties and constraints about objects and their spatial configurations, and a current model of the scene is proposed by the system. For architectural design, the complexity comes from the spatial configuration of objects and from the large amount of data. This observation explains why we are not interested in defining complex geometrical objects but in providing a high level description of object characteristics and spatial configurations.

Our model is composed of a 3-tuple where is the set of the scene objects, the scene hierarchical structure and L the set of locative relations and constraints between objects. A dynamic and interactive user interface is used to offer a high level interaction to the designer, and the dialogue is carried out by an object oriented language (figure 2). The verification of the scene description consistency and the proposition of a scene, solution of the description, are made during the resolution process.

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Figure 2: The system architecture

3 The Scene Hierarchical Structure

Each class of objects is a member of the following architectural abstraction levels:

1. urban,

2. building,

3 . architectural space,

4. architectural element,

5. architectural components,

6. architectural constructors.

The hierarchical structure of the scene is represented by a directed acyclic graph whose nodes are objects and whose arcs link an object to another one as a part of or as a copy of.

Definition 1: The object I is a part of the object J , if the abstraction level of the object I is inferior or equal to that of object J. This relation defines that the object I is a member of the object J structure.

Definition 2: The object I is a copy of the object J , if both objects are of the same class. The object I does not possess its own characteristics but is defined by those of the object J (except for its position and orientation).

For architectural design, the repetitive use of an element is usual. For example, in a six storied building, we d o n ’ t have to describe in detail all storeys if they are identical. So we must be able to make the description of only one storey, and then indicate that the others are something like a clone of this description. The copy link is only possible if the copy is identical to the original. When we


want to make a transformation on one storey only, the copy link must be replaced by a real copy of the storey’s description.

We have not associated a stronger semantics to this compositional model because the object structure is not static, and according to the positionning freedom of parts of an object, it is impossi- ble to infer a unique semantic relation between the object and its parts. There are not any internal localization relation, but this is replaced by direct reference to a part of an object by using tools for object designation either in a graphic view or in the structural graph, or by its own name. Thereby dialog between our system and the user requires a strong and high level interactivity.

In the example of figure 3, opening2 and room2 objects inherit opening1 and room1 object’s characteristics except their positions. The scene shown in the figure 3 corresponds to a structural graph where:

room1 and room2 are in front of the locator,

room2 is located on the right of room1 and they have the same front, back, top and bottom sides,

opening2 is on the right of opening1 and they have the same front, back, top and bottom sides,

Figure 3 : A structural graph example and a corresponding scene

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4 Objects

Each object refers to a particular class, and a class is composed of attributes, functions, methods and a prototype. Attributes denote characteristics of the object which can be represented by a variable of atomical or numerical type. Each attribute is described by a 3-tuple where N is its name, T its type and V its value. A function defines the object characteristics represented by an analytical inequation and is described by a 3-tuple where N is its name, Min and Max the two bounds of its validity domain, and C its body described by:

usual arithmetic operators

parenthesis (, ),

real constants,

basic geometrical constraints like volume, surface area, segment length, .

numerical attributes of the object and its components,

functions of the object and its components.

A constraint will be represented by a function of the object from which all parameters belong to part of itself. Methods correspond to qualifying adjectives, and permit to refine the description of an object. Each method is described by a 2-tuple where N is its name and P a sequence of predicates. These predicates can modify for example the value of attributes or the structural graph of the object.

Some attributes are predefined for every class of objects and represent characteristics useful for locative relation management and for the scene visualization. For example the attribute defining if an object is real or virtual offers to the designer the ability to represent a property by using a tridimensional object without any geometric representation: one can express for example a circulation zone by using a virtual object. Each object is defined in its own reference system of axes (see figure 4), which is oriented in the scene reference system by using the spatial view attribute which possesses four possible values (left side, right side, front and back view) with respect to its own intrinsic orientation and to the locator’s viewpoint. A bounding box with edges parallel to axis is associated to each object, and this box is defined by its position and dimensions. Dimensions of the bounding box are either fixed or included in a possible value domain or unknown, and its position depends on locative relations and geometrical constraints. Each object can be seen in its bounding box with its own parametric geometrical model, or like an object composed of other objects seen at a lower abstraction level. Photometric characteristics can be also associated to an object, like colour, texture, light source type, etc.

Figure 4: The object’s reference system


Certain object classes possess some particularities:

hole: An object of class hole is a virtual object (without any geometrical representation). The volume corresponding to the intersection of a class hole object with another object defines the extract part of this second object (like a boolean subtraction operation in CSG). This mechanism permits to preserve the user from object cutting and assembly operation which is a tedious task. For example, an opening in a wall is realized by putting an object of the class hole inside the object of the class wall with the same front and back side (figure 3), and the dimensions of the first object define the size of the hole in the second one.

locator: the object of this class is corresponding to a virtual person who is participating to the scene description from his position and orientation. During the design process, the user plays the role of the locator.

axis and frame: these objects are very useful for architectural design and some particular constraints are defined between them and other objects like symmetry or centering.

5 Locative Expressions

A locative expression involves a locative prepositional phrase together with whatever the phrase modifies [11]. Each locative expression is given in accordance with the current locator’s viewpoint. In our system, a locative expression is composed of a locative syntagma, a verb (to be) and two noun phrases: is locative syntagma The subject refers to the located entity and the object to the reference entity. Each locative syntagma possesses its own semantic defined in the relation reference system. The orientation of this reference system depends on the site orientation and for each locative expression, the site can have three kinds of orientation [12]:

1. intrinsic orientation: The site possesses an intrinsic part directed towards this direction (a wardrobe possesses an intrinsic front side).

2. deictic orientation: The site’s position with respect to the target depends only on the locator’s position and orientation. For example, in the relation the chair i s an f r o n t of the table, the chair position depends on the locator’s position and orientation and on the table position, because a table does not possess any intrinsic part.

3 . contextual orientation: The orientation is given by the target or another object external to the relation.

The description is given for a succession of locator’s viewpoints, and for each of them the locator is participating to the scene description: thus for each displacement, his last position is memorized by defining the locator object as a virtual object and by creating a new object for the actual point of view.

Locative relations are given on object bounding boxes, and the locative syntagma semantic [13] is expressed by one constraint along each axis of the relation reference system between edges corresponding to the projection of object bounding boxes (figure 5). Each constraint C(X, Y) corresponds to a disjunction of some Allen’s elementary relations [14], which permits to describe the relative positionning of two segment along an axis:

with and one of the thirteen Allen’s relations (figure 5)

For example the relation Object X i s o n the left of object Y is expressed in the relation references system by: where is the universal constraint and expresses that the thirteen relations are possible. The relative positionning of objects into the scene is corresponding to a conjunction of those constraints along each axis.


Figure 5: The thirteen relations between two intervals and the bounding box projection along the three axes

Locative relations can also be given on object’s sides with the following syntax:

a t a distance which is

Each side is represented along the axis parallel to its normal by a projection point of the side on the axis. The relative positionning of two parallel sides is expressed by a constraint on corresponding points (figure 6). A constraint c(x, y) between two points x and y along an axis is expressed by:

Each point x is corresponding to an extremity of a segment X . In the following and are representing the beginning and end points of the segment X . To have a unique representation for these two kinds of constraint, each Allen’s relation is expressed by constraints between extremities of segments:

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Figure 6: The three possible relations between two points

A description being a conjonction of constraints, each Allen’s constraint must be expressed in a disjunctive normal form to make the union of all constraints on the same segments or extremities, and among all Allen’s constraints there are only 187 ones wich are expressible on this form [15]. This could seem to be an important restriction, but in fact it is not. The explanation is that constraints expressible in a disjunctive normal form are corresponding to constraints which present a continuity in their geometrical configuration area. For example the locative relation The chair i s on the left or on the right of the table is not expressible in a disjunctive normal form on the lateral axis. On the other hand, the locative relation The box X i s on the table Y corresponding to and

is expressible in the following normal form:

where and is the set of object’s segments along an axis.

At any time and for each viewpoint of the locator, valid locative relations between objects and their sides can be calculated for each couple of objects. Let be the semantic of a possible relation between objects X and Y of class and respectively, and the existing relation between these two objects. After expressing the two relations in the same coordinate system, according to the position of the site object and depending on the actual locator view, if the corresponding relation is valid between the two objects. A graphical tool has also been developed offering to the user a graphical representation of the set of possible placements of the target object

Let be the set of constraints expressible in a disjunctive normal form. The thirteen Allen’s relation belong to and is closed for inverse, opposite, composition and conjunction operations, thus a description given by using Allen’s constraints expressible in a disjunctive normal form and constraints between sides, can be represented by the following formula along each axis:


according to the set of locative relations between the target and site objects, to the position of the site object and to the current locator view [16].

6 The Calculation of a Scene Description Solution

At any stage of the design process, a solution s, among the infinite set of valid solutions S, can be calculated and visualized. The solution calculation is achieved in two steps: the first step permits to check the consistency of the locative description and to obtain a minimal system of linear inequations; the second step adds to the previous system the set of geometrical constraints (object functions) and proposes one solution of the global description by minimizing an objective function subject to the global system of linear and nonlinear inequalities1.

1. From the set of locative relations, a directed valuated graph is constructed for each axis, whose nodes are bounding box edge extremities. Graph arcs are representing the relative positionning of points by using only < and relations, because if the logic relation between two points is (precede identical t o fo l low) or (precede fo l low) , there is no arc creation (the relative positionning of the two points becomes free), else if the logic relation between two points and is (identical to V fo l low) or fol low we use the opposite relation between and else if the logic relation is identical t o then the two nodes are merging. Each arc is valuated by the distance between its extremities, which is given by bounding box dimensions or by the distance between object sides. The consistency of this locative description is checked in a unique graph traversal by searching for circuit, which implies that any ordering is possible for points along the axis. A graph reduction process is done by applying a partial antitransitivity: each arc with an unknown length is removed from the graph when there is a path between its two extremity nodes. Some of the arc lengths are unknown, and it would be interesting to reduce the possible value domain by propagation of known values, but global propagation algorithms have a Non-deterministic Polynomial complexity. On the other hand, local propagation according to the local graph structure, is done with a weak cost.

2. A minimal system of linear inequations is obtained from the three graphs. This system is minimal because all equations are used to reduce the number of variables. Some geometrical constraints are linear, like relations between segment lengths, and are added to the previous linear system; the others form a vector of nonlinear inequations. This system can be well-constrained, but it is generally under or over-constrained; thus it is not possible to enumerate all solutions of the description. The translation of the problem into a system of linear and nonlinear inequalities allows us to solve geometrical and locative constraints simultaneously and to propose one solution among the infinity of possible solutions (when the description is consistent). The system is solved by using a resolution algorithm which minimizes a quadratic objective function F as follow2:

where is an by n constant matrix, and is an element vector of nonlinear constraint functions. A numerical solution of the problem is computed by using a NAG3 library routine, essentially identical to the subroutine SOL/NPSOL described in Gill et al [17].

The solution calculation is not completely detailed but is referred to a previous paper [13] ²This function permits to keep the equilibrium of the object's space distribution [13] 3NAG is a registered trademark o f the Numerical Algorithms Group Limited and The Numerical Algoritms Group

Incorporated.


7 Consistency of the Description

At every moment of the design process, an inconsistency can be generated by the description. Firstly we have topological inconsistencies due to an incompatibility between some locative relations. For example if in a room, there is a wardrobe, a table and a window such that the table is on the left of the wardrobe, which is on the left of the window, then if one says that the table is in the front of the window, it will produce a topological inconsistency which is easily detected by a topological graph traversal and expressed to the user. Secondly we may have some geometric inconsistencies: for instance when different values are given for the depth and width of an objet while one says this object is cubic. A part of this second kind of inconsistency can be detected during the construction of the global system and will be also easily expressed to the user. Other inconsistencies are detected during the numeric resolution process. The inconsistency explanation is more difficult in that case because information we get back is a set of inequations for which the value is out of bounds. We don’t have implemented a propagation mechanism yet to find reasons of this kind of inconsistency, which will necessitate to use rewrite rules on a formal version of inconsistent inequations. The system groups together inconsistent data into subsets possessing common variables, and produces these subsets to the user.

8 System Implement at ion and Results

A first version of this system has been carried out[16]. The object-oriented-language and knowledge representation model have been written in Quintus-Prolog and C++. The user interface is composed of a graphic zone written in Phigs included in a Motif window manager environment. The routine of the NAG library which makes the numerical resolution is directly called by prolog. We use a global illumination rendering algorithm [18] to obtain some realistic images of the scene. The following examples are illustrating our method.

The first example shows the management of objects whose some dimensions are unknown, and on which the user gives some constraints. The scene is composed of a carpet, a table, two chairs and the following description:

T h e carpet is two cent imeters high, f ive meters wide and three meters deep.

T h e table i s seventy cent imeters high and i t s width and depth are unfixed.

B o t h chairs are one m e t e r high and their width and depth are unfixed.

e T h e carpet i s in f ron t o f the loca tor .

T h e table and the two chairs are on the carpet.

Bo th chairs are respectively on the left and on the right of the table.

The scene solution calculated by our system is shown on the figure 7.

Figure 7: Initial solution of the first example


Adding a constraint defining that the table depth i s twice more important than width of both chairs modifies the scene only on the locator frontal axis (cf figure 8) because chairs are intrinsically oriented,

Figure 8: T h e table depth i s twice more important than width of both chairs

The figure 9 is obtained after adding a constraint defining that a quarter of the carpet area is occupied by both chairs and the table.

Figure 9: A quarter of the carpet area is occupied by both chairs and the table

The scene illustrated by figure 10 has been produced after the definition of the table width (two meters and eighty centimeters). In this scene, the area occupied by chairs has decreased proportionnaly to the increase of the table one maintaining the length relation on the locator frontal axis.

Figure 10: T h e table width i s equal t o two meters and eighty cent imeters

This example has shown that locative relations and geometrical constraints are jointly taken into account in our system, which allows us to constantly offer to the designer a solution of the global description as long as the scene description is consistent.

The second example illustrates that our system is useful even for more complex scenes through an easy description of a building. This building (figure 12) is composed of a ground floor, four identical storeys and a roof. On the front side of the building, each storey is composed of five identical rooms


Figure 11: Dimensions of objects (in meters)

with the same structure than on the figure 3: there are two identical openings in the front wall of rooms, in which a window is embedded. The ground floor is composed of four identical pillars, a winding stair and two rooms. Here are some locative relations in which objects of the ground floor are occuring:

e T h e wind ing s ta i r is se t on t h e left of r o o m 3 and in f r o n t of room2.

T h e top s ide o f t h e winding s ta i r is at t h e s a m e place as t h e bot tom s ide of the door .

e T h e r ight s ide o f t h e door i s on t h e left of the right s ide of room2 at a distance which is included in a possible value d o m a i n [0.2,0.3].

T h e locator is in f r o n t o f t h e d o o r .

Dimensions of objects are given in the figure 11. Because of the copy of links, some geometrical constraints (lengths equality) are implicit for rooms, storeys, windows and pillars. There are also two other geometrical constraints:

e

Conclusion

This paper has presented our declarative design methodology which provides the ability to manipulate uncertainty in both numerical and locative constraints. The description of objects at a higher level than the geometrical one and the use of prototypes permit to reduce the decomposition/recomposition step. Examples have illustrated the ability of our system to deal jointly with topological and geometrical knowledge. One of its main characteristics is the cooperation between two inference techniques which are most of the time competing: on the one hand a logical inference stemming from Allen’s temporal logic and instant logic, on the other hand a numerical inference based on an optimization under constraints algorithm. We are currently extending this model to more complex geometrical objects, and we are investigating other design domains involving new kinds of constraints.

S. Donikian et al. /A Declarative Design Method for 3D Scene Sketch Modeling C-235

Figure 12: The building of the second example

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