Thursday, September 22, 2022

Tribute to Godfried by Luiz Henrique de Figueiredo

I was first in touch with Godfried Toussaint by email when I was working on my PhD, over 30 years ago. From him and his books I learned about computational morphology, which I used as the theme and title of my thesis "Computational morphology of implicit curves", later published in The Visual Computer as Computational morphology of curves. I met him briefly in 2001 at the Canadian Conference on Computational Geometry in Waterloo, when I gave a talk also based on his work: Good approximations for the relative neighbourhood graph. On both occasions, he was very kind, ready to give free advice. Indeed, he was one of the kindest people I've known.

I have recently published a paper dedicated to his memory in Computers & Graphics: Region reconstruction with the sphere-of-influence diagram. In that paper, we introduce the sphere-of-influence diagram of a set of points in the plane: it is the planar diagram induced by intersecting the sphere-of-influence graph introduced by Toussaint with the Delaunay triangulation. Surprisingly, to the best of our knowledge this natural diagram has not been studied or used before. We use the sphere-of-influence diagram for region reconstruction from point samples. I hope it's a fitting homage to a computational geometry pioneer.

Tuesday, November 12, 2019

Tribute to Godfried Toussaint by his former PhD student, Binhai Zhu

It was a shock when a colleague told me Godfried's sudden passed away.
I was Godfried's first Chinese PhD student. My story with Godfried was
sort of a drama, even though I never collaborated with him again after
my graduation in 1994. What happened during my stay at McGill
(Sep, 1991-June, 1994), especially in late 1991, changed my life completely,
both academically and socially.

I was admitted to the PhD programs at both McGill and Dartmouth in 1991.
I turned down McGill and went to Dartmouth initially. Being used to big cities
like Beijing and Toronto, I was not able then to deal with a 7000-people small
town (Hanover, NH) and felt bored and restless (it was a very small PhD program
then at Dartmouth). Arriving at Hanover in early September and after a few days,
over a boring Thursday afternoon, I dialed his number using a coin-operated
payphone in the graduate activity room --- such a vivid scene even today! I
didn't remember what I exactly complained but I still remembered his commanding
voice "Binhai, the semester already started, come back immediately!". I packed
my stuff and drove back to Montreal over the weekend.

In the early 1990s, at McGill all the PhD students had two chances to take and
pass a tough qualifier exam. Being a graduate student with some research
experience already, I wanted to start my research immediately even though I had
to prepare for the qualifier exam at the same time. I tried to select some
topics for my thesis research, but failed a few times, each after some intensive
bibliography reading. One day in the middle of October, seeing his office door
open, I knocked softly. Godfried raised his eyes and asked me how everything
was going. I told him about my puzzled feeling of being unable to find a
research topic. He replied "I remember Micha Sharir had a paper on terrains a
few years ago, and I felt there was something there!". Without any waiting, I
went to the McGill library, searched the database (no internet web browser
then!), read and photocopied Sharir's 1988 IPL paper on the third floor. By
the time I walked out of the library, in less than an hour after talking to
him, I already had an idea to slice off a log factor over Sharir's
bound --- this was the basis of my PhD thesis and the O(n log n) time algorithm
for the shortest watchtower problem is still the best today in 2019!

Godfried was sharp on identifying new research problems, so far one of the two
best people I have ever collaborated in that aspect. Teaching in a classroom,
he would sometimes suddenly stop and ask "Why must we study this problem? Could
we have a different problem?". And in several occasions this triggered his 
graduate students to research on these new problems, an example being the
'Unoriented Theta-Maxima' paper later published in SIAM J. Computing, initially
triggered by his classroom question "Why we have to restrict the maxima to be
rectilinear?". One of his casual but cutting edge opinions, "Finding problems
is sometimes more important than solving a problem.", deeply changed my way of
doing research, especially when I myself started to supervise PhD students
(some in areas out of geometry).

I left McGill in 1994 and after that I never collaborated with Godfried again,
partly due to my shift from computational geometry (though I never really gave
it up). But Godfried was always with me in different ways. We met irregularly
at conferences since 1994, and we lastly exchanged emails in 2017 about
finding a chance for me to give a talk on computational genomics in Abu Dhabi
(so that we can meet again!). This is not to happen. On the other hand,
maybe this is not really a pity as some part of Godfried, his mind, thoughts
and more, will be around in this world for a long long time, and I can feel it!

Godfried, you will be deeply missed!

Friday, October 11, 2019

Tribute to Godfried by Greg Dudek

I was a colleague of Godfried's at McGill for something like 25 years. 
When he was on the committee that hired me, he scared the hell out
of me.  This was not because he was unfriendly in the least, but rather
because he was so sharp and intellectually demanding.  That spirit of
excellence was something he maintained with unwavering dedication, and
it was something I came to deeply appreciate as his colleague.  As a
member of the department, there were only certain things Godfriend was
willing to do, but those things he took on, he accomplished with
complete dedication.

Along with his close associates, he exemplified a style of intellectual

freedom and creativity that has rarely been matched.  His panache was
exemplified in his professional life, his personal life and his daily
choices.  When he left our university, we lost a vital and exciting
spark.  Now the world as a whole has lost that too.

Tuesday, October 8, 2019

Photos from JCDCG

Hiro Ito sent these memorable photos of Godfried from past JCDCG conferences in Tokyo:

JCDCG 2002: Banquet in Tokyo, December 4, 2002

JCDCG 2004
Left: Crab restaurant in Okhotsk, October 5, 2004
Right: Frozen towels in the museum of Okhotsk, October 6, 2004

Sunday, September 22, 2019

Tribute to Godfried by Susan Gerofsky

I met Godfried in January 2007 when I was a very new assistant professor of Mathematics Education at the University of British Columbia. I had been invited to a Bridges Math and Art symposium at the Banff International Research Station, my first introduction to the wonderful Bridges community.

Godfried, David Rappaport, Paco Gomez and I spent lots of time together there, working out relationships among circular representations of musical rhythmic patterns, spirographic designs, aspects of number theory and abstract algebraic necklace problems. We had lots of snowy walks down into town to a cafe and to the dollar store to buy geometric toys. Our musings resulted in a paper together for Bridges 2009.

Throughout the process of exploring and writing our findings, I was immensely grateful for Godfried's generosity, curiosity, enthusiasm and kind mentorship. I learned a lot, and was welcomed into the work that Godfried, Paco and David were already doing together. Our experience at Banff remains an example for me of the best ways that senior and junior researchers can work together across areas of expertise, with friendship, humour and productivity.

It was a shock to hear of his passing just today. We will miss him a lot.

Innovations in Mathematics Education via the Arts
BIRS, Banff Center, Alberta, Canada
Group Photo January 2007

Thursday, September 19, 2019

Tribute to Godfried by José-Miguel Díaz-Báñez

Godfried Toussaint, one of my three academic parents, you were the promoter of the Spanish Meeting of Computational Geometry, the Rocio’s workshop, the Cofla project (math and flamenco music and many other advances in research on geometric algorithms in Seville and Spain. Thank you very much for everything you gave us, Godfried. I’m sure you will be with Ferran Hurtado working on nice problems in some charming place. We will never forget your way of looking for beauty.

Saturday, September 7, 2019

Photos by Yushi Uno from Barbados 2019

Thanks to Yushi Uno, here are some great photos of Godfried thinking, working, and playing at the latest Bellairs Workshop on Computational Geometry that we co-organized in March 2019:

Wednesday, August 28, 2019

Tribute to Godfried by David Bremner

I was a PhD student at McGill in the mid-1990s, where Godfried was a
mentor and a friend to me. My PhD thesis went off in other directions
from the Euclid inspired problems that Godfried loved the most, but
Godfried was nonetheless a co-author on my first journal publication.

I first really got to know Godfried when I was invited as a Master's
student to his Bellairs Workshop Computational Geometry.  I got two
things out of that first workshop; the first was a radical (although I
didn't know it at the time) understanding of how collaborative and fun
research could be, and the second was a love of scuba diving.  Others
have describe Godfried's laid back attitude on land; if anything this
was even more true underwater. Godfried was a natural athlete, and his
inquisitiveness and love of beauty was also evident while diving and
while talking about the day's discoveries.

I'm late sending these brief words to acknowledge Godfried's impact, so
much of what I might relate has been said by others. Let me close by
saying that what was most remarkable about Godfried was not the
friendship and collaboration he offered us individually (although don't
get me wrong, that was remarkable), but the way that he acted as a kind
of one-person social network. Many collaborations started at a workshop
(or simply a coffee shop outing) organized by Godfried, and many of us
writing to this page became collaborators and friends at least partly
because of Godfried.  I can't remember decades later how directly
Godfried was involved in writing a slightly scandalous (or so we
thought, in those innocent days) rap song to commemorate Paco's time at
McGill, but I know he helped nurture the community where that seemed
like precisely the right way to finish up a postdoc.

Sunday, August 25, 2019

Remembering Godfried Toussaint by Suneeta Ramaswami

I first got to know Godfried Toussaint when I was a postdoc at McGill University too many years ago. Godfried's office door was always open, ever ready for one of his students or colleagues to stop by to discuss a problem, preferably over coffee or lunch or dinner. I was lucky enough to attend several of his Bellairs workshops, a welcoming and inclusive work environment through which I met many research collaborators as well as friends. Godfried was an extraordinary computational geometer, a founding member of the field, and a relentless problem poser and problem solver. But above all else, Godfried believed that research was as much a social enterprise as it was an intellectual one. He exemplified the philosophy that research is a lot more productive and enjoyable when it is done collaboratively with others.

I hadn't seen Godfried in a few years, but I always imagined that he was continuing on with his usual vibrancy and energy and joie de vivre. I feel very sad now that we did not get a chance to meet more recently. 

Rest in peace, Godfried.

Wednesday, August 14, 2019

Tribute to Godfried by Vera Sacristán

Godfried was an inspiring person for me. And for the entire Spanish CG community. He enjoyed exploring new problems and finding (apparently) simple solutions for them. He strongly believed in collaboration, as he proved in many ways. His Bellairs workshops have influenced the entire CG community. Only for that we already owe a great deal to him. Not to mention his scientific contributions and his always friendly attitude. He was tolerant and passionate at the same time, a very rare combination. We will miss him very much!
Godfried proposing new open problems just this year at Bellairs. Picture by Zuzana Masárová.

Tuesday, August 13, 2019

Remembering Godfried by Selim Akl

I first met Godfried in the summer of 1975. For the next 44 years I called him my friend.
As a graduate student in the School of Computer Science at McGill University, I enrolled in a sequence of courses taught by Godfried. He introduced me to the fascinating world of computational geometry, a field still in its infancy in the mid-1970s.

Godfried was only four years older than me and we shared many interests, algorithms of course, but also music and theatre. And we were both single. Every evening, when everyone at the School had gone home, there were two people left in Burnside Hall, Godfried and me. We worked, separately or together, until one of us asked if the other wanted to go out for dinner. Most times we ended up at the Basha where we enjoyed Lebanese food while solving geometry problems on the paper napkins. It was great fun, especially when we relished in discovering counterexamples to published algorithms.

The first problem we worked on together was the convex hull and this led to my first ever journal publication. Later, we began a book on convex hull algorithms, but eventually our interests took us elsewhere and sadly this project was never completed.

Godfried was a researcher who had an amazing ability to get people excited about problems. His flashes of intuition were spectacular and hard to resist. We all wanted to keep up. We wanted to be part of this exciting adventure. He was a leader and the founder of many areas of research in computer science. As this tribute page testifies, he supervised numerous graduate students who have gone on to become influential academics in their own right, as well as industry leaders. Many of his papers are landmarks, and some of his ideas opened up entire new directions of investigation. His writing is an example of engaging and lucid prose. Generations of researchers were inspired by his pioneering work in computational geometry. His originality, his creativity, and his boundless energy and enthusiasm for knowledge are legendary.

Godfried and I collaborated on many research projects over the years, and I was always impressed, not only by his quick and brilliant mind, but also by the generosity of his spirit, and his immediate willingness to share credit for an achievement.

In 2017 when a group of colleagues kindly decided to put together a Festschrift for me, Godfried was the first to submit a paper entitled Simple Deterministic Algorithm for Generating “Good” Musical Rhythms, which appeared as the first chapter in the volume.

When, for Christmas 1980, my future wife and I took our first trip together, we were Godfried’s guests at his home in Montreal. He was a most courteous and generous host. In those days, Godfried was an active and talented dancer, and belonged to a ballet jazz group. It was a thrill to watch him dance. On the occasion of our visit, Godfried and a friend performed for us, in his living room, to the music of Prélude à l’après-midi d’un faune by Claude Debussy. It was magical and unforgettable. In July of the following year, Godfried was a guest of honour at our wedding.

Dear Godfried: I miss you already, rest in peace my friend.

Friday, August 9, 2019

Tribute to Godfried by Greg Aloupis

Υστεροφημία (Ysterofimia). This is a word that describes one of the greatest desires of ancient Greeks. To be remembered well, eternally.  I have no idea if Godfried cared about this, but it is a word that leaped to mind when thinking about him in recent days. Godfried’s way of life and influence on all of us will be remembered and missed. In this sense, he will remain immortal. 

When I started my MS degree, I had only taken a few basic courses in CS, and planned on jumping into the field of mobile robotics, coming from my physics undergrad background. In the first week of my first semester I shopped around for courses, attending as many as possible. One of those was the mysterious Computational Geometry, taught by Godfried. I was instantly hooked.  I loved the material, the teaching style, the enthusiasm that Godfried had. By the end of the week I knew that I wanted to focus on his course. His homework problems were incredibly fun, and many were quite difficult.  I recall walking up to Godfried at the end of a lecture when the first assignment was due. I shyly asked him what the solution was for a particular problem that I couldn’t solve, hinting that I was a bit concerned. He smiled and said not to worry, nobody ever solves that one. 

By the end of the semester I couldn’t wait to take Godfried’s Pattern Recognition course, which included a project that eventually turned into my MS thesis.  After that first year, when I officially became Godfried’s advisee, a whole new world opened up for me.  Through Godfried I got to know the McGill theory group, and became part of the Bellairs crowd.  I had no idea that academia could be so much fun, both in terms of research and socially.  The lunches at McGill were often the highlight of my day, listening to hilarious and wild stories by Godfried, David and Luc.  So were the evenings at Bellairs, when we would all sit together under a tree, Godfried with his cigar and glass of port.  In general, wherever we went, Godfried’s circle of friends always created an exceptional environment, on the convex hull, as he would say.  So I have often thought about how lucky I am to have met him, to have followed this random path that led to meeting so many lifelong friends and to great adventures.  

Godfried’s lecture style directly influenced mine. Students often ask why I handwrite my course notes, and I inevitably pause to describe Godfried’s projector, with all his overlapping slides taped together in a way so that he could flip slides over from all four directions and make shapes ``grow” and ``move”.  Godfried taught in a way that kept you on your toes the entire time, not only because of his visuals but because he would let us explore incorrect ideas for ages until we discovered that something was wrong. I now do this in my own C.G. course, and it makes me happy to tell students that this was how I learned from Godfried, back in the day. 

Throughout my MS and PhD, Godfried gave me an ideal mix of support, encouragement, and independence. I have always been thankful for this, and for the chats that we have had about non-academic matters, both during that time and the many years that followed. He has given me advice that I have followed daily. I can’t imagine how life would have been without his influence, nor do I want to. I wouldn’t trade it for anything. 

Godfried, I owe so much to you. Thank you for your friendship.

Thursday, August 8, 2019

Tribute to Godfried by Teresa Mejón (widow of Ferran Hurtado)

Al conocer por Jit Bose la triste noticia del fallecimiento de Godfried, me uno
al homenaje que compañeros, amigos y discípulos le tributáis, tanto por el gran cariño
y admiración que Ferran sentía por Godfried, como por la pena que yo siento por su

Ferran, en 1990, durante el postdoc en McGill, asistió a algunas clases y sesiones de Godfried, a partir de entonces siempre reconoció que el estilo personal de Godfried,tanto a nivel de trato con el alumnado como por su manera de plantear la investigación, lo habían marcado decisivamente. Y como esto coincidió con los inicios de la etapa investigadora de Ferran, este influjo estoy segura que pasó a otros matemáticos que nunca conocieron a Godfried.

Además de las matemáticas, yo fui testigo (ya que Godfried hablaba un estupendo castellano) de que muchos otros temas los unían y hacían posible que yo me uniera a ellos, de manera especial la música y la literatura clásica. Siempre era una gran alegría cuando
venías a Barcelona.

Godfried, allá donde estés, recibe mi más cariñoso homenaje.

Teresa Mejón (viuda de Ferran Hurtado)

Tribute to Godfried by David Rappaport

I was lucky enough to be a graduate student of the School of Computer Science at McGill in the early eighties. It was there that I enrolled in a grad course with the nondescript title: “Topics in Computer Science”. Godfried taught the course and on the first day he gave it more descriptive title: “Thinking and Creating Knowledge”. For anyone who has had the pleasure of attending one or more of the many workshops that Godfried organized the title makes perfect sense. The Godfried Toussaint workshop where people gather to think and create knowledge have become legend.

Godfried was master at “thinking and creating knowledge”. As students we were required to solve an open problem in the course. It could be a problem of our own invention or one of several problems that Godfried suggested. We met and thought and some of us quit, and others came back and thought some more. There were seminars that we had to give. And always the thinking and creating. By the end of the term I and most of the others solved some of the problems. My problem turned out to be my PhD topic, and that was also true of others in the course.

I have attended too many of Godfried’s workshops to count. There is no question that we had fun at those workshops. However, I also know that behind the laid back facade Godfried would wake up early and stay up late working hard writing, or polishing, or reviewing, or thinking about the next new topic.

Godfried was a fountain of creativity, his ideas about exploring some new topic, or looking at known topics in different ways, came from him seemingly endlessly. It’s one thing to have the ideas, but Godfried also had a way of convincing others that his latest new idea was interesting and worthy of exploration.

We also played in a together in a band. The Algorhythmics rock band. Godfried as the drummer provided a rock solid bed which supported the rest of the band. That’s what Godfried did. He provided rock solid support that helped us do our best.

Godfried worked hard and played hard. I haven’t seen him in years, likely since he moved to Abu Dhabi. I now wish that I visited him there. Because now I miss him very much.

On the beach in front of Godfried's first workshop in 1986.

Tribute to Godfried by Marc van Kreveld

My first encounter with Godfried was when he visited CWI in Amsterdam 
(for a sabbatical I think), around 1989. Mark de Berg and I took his 
computational geometry class, after having taken the one of Mark 
Overmars a few years before during our studies. While Mark's class 
followed the book of Preparata and Shamos closely, Godfried's class was 
more free and we learned a lot of new things.

A few years later I got to know Godfried a lot better, when I did my 
postdoc at McGill University in 1992/1993. This was a very fun and 
productive year. I got to work with many of the people at McGill and 
nearly universities, including Sue Whitesides, Jit Bose, David Bremner, 
Jean-Marc Robert, Hazel Everett, and of course Godfried Toussaint. I 
remember that Jit, Godfried and I were working on a casting problem and 
used an orange peel to understand what the geometry of the casting 
problem was. It was a memorable year for me (in a positive way of course).

Many years later, in a furniture store in Utrecht that specializes in 
modular book shelves, I was looking at the books they had standing in 
the showroom to decorate their products. I was very surprised to see a 
familiar book: Godfried Toussaint's Computational Morphology. It seemed 
fitting to me, that such a book decorated the shelves of book shelves 
whose geometry could be changed at will. I guess very few customers 
realized how much this book had meant to the computational geometry in 
the early days.

I will remember Godfried for the gentle person he was, and his great 
interest in all research in geometry.

Sunday, August 4, 2019

Tribute to Godfried by Paco Gomez

Godfried’s death came to me as a very painful surprise. As in the case of others, Godfried was friend, teacher, mentor, and adventure mate. But before anything else, he was a friend, a very good friend. I met him in 1992 at McGill. Soon his love for research and especially his approach to it made a great impact on me. I came from a place where research was conceived as an individual work that you would do with your supervisor, almost secretly, where only the results were important (you weren’t important). With Godfried, however, research was about beauty and fun. He conveyed that sense of beauty through a fierce passion for the subject as well as excellent communication skills (he was a great orator and writer). He was able to raise above the sea of results in the area and spot new virgin territories where to extract new and exciting problems.

Godfried also was a polymath. He was a musician and so was I, and very soon we connected and started to play together back in 1992. He’d visit me in Madrid on a regular basis and every time he was in town I organized some kind of gig, concert, show with more friends (Giovanna, Shima, Stefan, Andrew). I remember that we started to do research in Mathematical Music Theory at the same time, around 2002. We had so much fun by doing so! He’d invite me to his Bellairs workshops, where I met so many fascinating researchers. Among other Godfried’s interests, we find dance, literature (he wrote a couple of novels), cinema, sports.

Another distinctive trait of Godfried was his sense of humor. He was always laughing. He could find reasons to laugh about in the smallest details of daily life, so good-humored he was! When I first met him, I happened to have an obsession for water guns. I’d like to squirt people with small water guns pretending I was sneezing or something along these lines. I challenged him to go to a bar and squirt the patrons just to see their reactions (sometimes we’d aim at the most beautiful women in the bar just to strike up conversation with them). And he’d follow down my crazy paths. We laughed like hell. He was that type of guy.

The last one indelible impact Godfried made on me was of social nature: the way he interacted with students. Godfried treated them as their peers in the adventure of learning. More important, he treated them as human beings, and considered that every single student had very valuable things to put on the table. I remember with great joy the lunches that we had together, him and other students, every single day of workweek. We discussed research problems, laughed, talked about our worries, personal and otherwise; in a nutshell, we celebrated life and the human condition.

Yes, Godfried was good at living life. Thank you, friend. I miss you.

Friday, August 2, 2019

Tribute to Godfried from Tamal Dey

I was never directly connected to Godfried in any capacity of being a collaborator. However, in my early years, when I was just learning about Computational Geometry, some of his work did inspire me. I specifically remember his work on relative neighborhood graphs. It was a simple but powerful idea. I would also like to reminisce an incident here. In 1995, we had a SoCG paper titled `Visibility with One Reflection'. After the presentation of the paper (by one of my co-authors), Godfried commented that this is an excellent work. He did not tell it directly to me, but I heard him talking about it during the Coffee break. As a new comer to CG, hearing such a comment from a stalwart enthused me so much that I still remember that incident.

It's a great loss for CG. May his soul rest in peace!

Thursday, August 1, 2019

Tribute to Godfried by Binay Bhattacharya

I remember and admire Godfried for his profound creativity and his superb teaching abilities. My years at McGill in the late seventies were a pivotal time in the development of Computational Geometry. In the decades since Godfried remained at the center of the field in his own research, and in communal leadership. Godfried championed the growth of Computational Geometry in Canada, inspiring generations of students. Today, much to Godfried's credit, almost every university in Canada has at least one faculty member researching geometry-related areas.

In terms of innovation in research, I have never seen anyone else who generates problems as interesting as Godfried did. His body of work is prolific and varied. His foundational research in Computational Geometry has inspired extensive further contributions in the field. Godfried's latest work on analyzing the rhythms of traditional world music using tools from computer science, mathematics, music theory, and computational biology is a fine example of his exceptional ability to pursue ideas and connections to their fullest potential. He had the knowledge base and expertise to pursue common threads connecting seemingly different topics, and he did so freely, and with fascinating results.

I have never had a better teacher, mentor, or colleague than Godfried. Godfried's vision continues to be a strong influence on my work. With a heavy heart, I say, "Goodbye Godfried. May your soul rest in peace. Hope to meet you again in the next life"

Wednesday, July 31, 2019

Tribute to Godfried from Erik Demaine

A father of the field and a father figure to many of us.  I wasn't a student of Godfried's, but while I was a student at Waterloo, Godfried invited me to visit him several times at McGill, both the Montreal and Barbados campuses.  Over the years, Godfried showed me (and everyone) a deep warmth and caring.  He also taught me a lot, from geometry and mathematics to history to music/rhythm theory.

But the biggest lesson I learned from Godfried was the importance of collaboration.  Working on math problems in group brainstorming is both way more productive and way more fun, making research into a social experience.  This lesson completely transformed and continued to shape my career (and hopefully also my own students).  Now almost all of my research happens in the group brainstorming environment that Godfried exemplified.

The epitome of this collaborative spirit was Godfried's famous Winter Workshop on Computational Geometry, which reached its 34th year this year.  I attended this workshop every year since I was 18 years old, and in recent years had the priviledge of co-organizing the workshop with Godfried.  It was great to see him one last time at the workshop this year, 20 years after my first Winter Workshop.

Some of Godfried's early papers in computational geometry were counterexample papers, revealing critical bugs in previously published papers that he'd read carefully.  He once told me that his goal was to uncover mathematical truth, so he was surprised when he found that his counterexample papers upset the authors whose algorithms he was disproving.  Once he discovered this fact, he vowed to never write another counterexample paper, instead writing to the authors directly and finding a more polite way to set the record straight.  So I was excited when I and my students found a bug in one paper of Godfried's, and Godfried made an exception: together we wrote Godfried's final counterexample paper, featuring a counterexample to his own paper.

I'll miss you, Godfried.

Me with two dads, at CCCG 2004.

Tribute to Godfried by Manuel Abellanas

The Spanish CG community is indebted to Godfried Toussaint. He has been a promoter of the field in Spain. Many of us had the benefit of sharing work and social experiences with Godfried. He had the ability to propose interesting problems and share brilliant ideas with everyone. He was elegant, polite and charming. Let's raise a glass of good wine in his honor!

Tribute to Godfried by Joseph O'Rourke

I met Godfried at a pattern recognition conference around 1980, and he invited me to McGill to give a talk. It was there that he introduced me to art gallery theorems. I immediately abandoned my pattern recognition work and focused on art galleries, with considerable help from Godfried. For example, it was his idea to generalize guards to mobile guards, patrolling an edge. And, as Joe Mitchell mentions, he introduced what has become known as GFP, “Godfried’s Favorite Polygon,” to show that the boundary can be completely covered by vertex guards while leaving interior points invisible:

A few characteristics:

  •  He loved counterexamples such as the GFP, and in fact several of his papers have the title, “A counterexample to …”
  • He was a scholar par excellence: he read everything, and had a near photographic memory. His bibliographies were always extremely long.
  • He was immensely creative in finding rich research areas for his beloved Bellairs workshops. Even at this past March’s workshop he raised a question asking for the probability that a 4-bar linkage is Grashof.
  • He was a great and fast writer. Once at one of his Bellairs workshops, on the final day when everyone was milling around, he sat down and penned (literally penned) a paper from start to finish. And his first drafts were only epsilon from final drafts.
  • As Jit mentioned, he insisted on the broadest possible notion of collaboration, instituting the rule that everyone at his workshops was by default a co-author on every paper (all listed alphabetically), unless they withdrew their name. The CompGeom community to this day continues Godfried’s tradition of collaboration.
  • He had a great sense of humor, introducing (in Barbados of course) sail polygons, crab polygons, and palm polygons:

He truly is the father of computational geometry, co-starting both SoCG (with me) and CCCG (with David Avis).
He changed my life by introducing me to CompGeom, and then mentoring me for nearly forty years. May we all strive to follow the high standards he set for our community, for in that way Godfried lives on.