Methods for Sculpting Digital Topographic Surfaces Dissertation zur Erlangung der naturwissenschaftlichen Doktorwürde (Dr. sc. nat.) vorgelegt der Mathematisch-naturwissenschaftlichen Fakultät der Universität Zürich von Caroline Young Westort aus den Vereinigten Staaten von Amerika Begutachtet von Prof. Dr. Robert Weibel Dr. Stephen Ervin Prof. Dr. Kurt Brassel Zürich 1998 Die vorliegende Arbeit wurde von der Mathematisch-naturwissenschaftlichen Fakultät der Universität Zürich auf Antrag von Prof. Dr. R. Weibel und Prof. Dr. K.Brassel und als Dissertation angenommen. Curriculum Vitae Name: Westort Vorname: Caroline, Young Date of Birth: 26. September 1964 in Massachusetts, USA Hometown: Massachusetts, USA Education 1973 – 1979 Primary and Secondary School in Amherst, Massachusetts 1979 – 1982 Amherst Regional High School Diploma 1982 – 1986 Bachelor of Arts, Bowdoin College, Brunswick, Maine, ma jor: Chemistry, minor: English. 1993 Masters Degree, Landscape Architecture (M.L.A.) Advisor: Prof. Stephen Ervin, Harvard University, Graduate School of Design. Thesis Title: “Designing Digital Topography”. 1994 – 1998 Research Assistant and Doctoral Candidate with Prof. Dr. R. Weibel, Dept. of Geography, University of Zürich, Dr. Stephen Ervin, Harvard University Graduate School of Design, Prof. Dr. K. Brassel and . Dept. of Geography, University of Zürich. Lecturers K. Steinitz, W. Mitchell, M. McCullough, S. Ervin, K. Brassel, R. Weibel, M. Heller, R. Forman, M. Benes, M. Binford, D. Schodek, M. Hays, P. Walker, G. Hargreaves, E. Meyer, M. VanValkenburgh, M. Wethli, G. Bruno, D. Page, E. DeLamotte, P. Litvak, M. Reizbaum. Copyright Copyright ©1998 Caroline Young Westort All Rights Reserved. i ii Abstract Abstract This investigation offers an argument and demonstration of how two seemingly different graphic representations of terrain are formally equivalent, and how when they are coupled with a data structure and computer algorithm for convert- ing from one to the other new kinds of digital sculpting may be undertaken. The thesis defines a generic digital topographic surface sculpting tool which incorporates concepts native to the artistic endeavor, sculpting, and which offers unique advan- tages over other common approaches to digital surface manipulation. Implemen- tation of the key components of this definition serves as a proof of concept for evaluating the merits of this approach. The thesis makes three primary research contributions. The first is a formal- ism which starts with an interdisciplinary survey of relevant literature and meth- ods of manipulating digital and non-digital surfaces. The traditional (non-digital) sculpting processes looked at are: carving, modelling, construction of objects, casting and moulding, and kinetic sculpture and arrangements. From this survey, a basic definition of the sculpting endeavor is devised; the constituent parts for which in- clude the following four universal components: tool, material, method, and simul- taneous multiple degrees of freedom. Each element of this basic definition of sculpting is then discussed individually in order to tailor a generic (and imple- mentable) definition of a digital sculpting tool. The second research contribution is the definition of the generic sculpting tool itself. The definition consists of four components: (1) a shape, (2) a path, (3) a relationship between shape and path characterized by orientation (angle and track point position) and static and dynamic mode, and (4) the effect, or result of the application of a shape to a path, which is ultimately an addition to and/or sub- traction from the surface. Effect’s parameters include its scope of action, which distinguishes between local, regional and global moves and passes, together with a formalism for corner, overlap and end options. Significant is that the definition is a simple and compact one. It encapsulates all of the necessary parameters nec- essary for defining any surface geometry, not only topographic surface geometry. It also offers mathematical and geometric equivalence – for every surface and path together with their relationships there exists exactly one surface geometry which may result. The definition also does not include the surface representation itself, i.e. its surface defining parameters are decoupled from the digital surface represen- tation (raster, TIN, contour lines, etc.). The alternative internal representation of a surface that is instantiated by this definition is therefore a very compact and simple one. The third research contribution is the demonstration of the ideas via an im- plementation of a raster-based prototype software, Topographic Surface Sculptor (TSS). Base class equivalents to the generic tool design’s components are devised. They are: CTool, CShape, CPath, CEffect, and CTarget. The prototype implemen- iii Abstract tation demonstrates the conceptual simplicity of how extrusion of two lines to- gether may create geometrically very complex surfaces which are easy to change, and at the same time intuitively straightforward for a user to generate and control. The fourth research contribution is a conceptual discussion of the implica- tions of this approach on ways of thinking about traditional sculpting in general. The generic digital sculpting tool definition encapsulates traditional sculpting’s requirement for a material and a tool into one internal digital representation. This coupling of tool and material suggests ways of sculpting which remain un- explored in any media, and merits further exploration in the digital domain. iv Table of Contents Copyright ................................................................................................................... i Abstract .................................................................................................................... iii Table of Contents................................................................................................... vi Acknowledgments................................................................................................. ix Dedication................................................................................................................ xi Chapter 1: Introduction 1.1 Motivation ......................................................................................................................... 1 1.2 The Problem ..................................................................................................................... 1 1.2.1 Previous relevant work ...................................................................................... 4 1.2.2 GUIs alone are not the answer.......................................................................... 8 1.3 The Approach................................................................................................................... 9 1.4 Research Objectives & Organization of this Thesis............................................. 11 Chapter 2: Landform as Expressive Medium 2.1 Introduction .................................................................................................................... 13 2.2 Landform Construction Tools.................................................................................... 13 2.2.1 Excavation Tools and Machines ..................................................................... 14 2.2.2 Level Two; Specific Landform built by Excavation Equipment.................... 19 2.2.3 Gardening Equipment...................................................................................... 20 2.2.4 Agricultural Equipment.................................................................................... 24 2.2.5 Topographic Manipulation in Professional Practice ..................................... 24 2.3 Descriptions of Landform ........................................................................................... 26 2.3.1 Contour signatures........................................................................................... 26 2.3.2 Drainage patterns............................................................................................. 29 2.3.3 Geomorphology / Geomorphometry.............................................................. 30 2.3.4 Organic vs. Chrystalline forms........................................................................ 34 2.4 Conclusions .................................................................................................................... 38 Chapter 3: Towards a Definition of Sculpting 3.1 Introduction .................................................................................................................... 41 3.2 Relief Sculpture vs. Sculpture in the Round.......................................................... 41 3.3 Sculpture vs. Sculpting ............................................................................................... 43 3.3.1 Sculpting as Verb ............................................................................................. 44 3.3.2 Truth to Materials and Working Direct; The Onset of Modernism............... 46 3.3.3 Sculpting as Subject of Sculpture................................................................... 48 3.4 Carving............................................................................................................................. 49 3.4.1 Finishing Tools ................................................................................................. 52 3.4.2 Other Subtractive Techniques........................................................................