Blocking Your Path

A couple years ago, my wife and I picked up some colorful blocks at a toy store. Each block is a quarter of a cylinder. The square faces of the blocks snap together with help from two magnets inside. There are just enough blocks in the set to make this fascinating shape: I’m struggling to […]

FabLearn 2020 Demo

A collaborator and I had a short paper on programmatic fabrication accepted at FabLearn 2020, and we’re presenting that work in a demo session on Zoom next weekend. Herein I walk through some of the example programs that we plan to work through with our visitors. Button Let’s start with a practical example—one inspired by […]

Timing in Twoville

Twoville serves two very different domains: physical fabrication and digital animation. Fabricators use Twoville to describe static geometric shapes that can be fed into a cutting machine and turned into a tangible object. Animators use Twoville to orchestrate purely virtual cinematic progressions in which the actors are geometric shapes. The thread binding these two domains […]


Deriving the View Matrix

Computer graphics is less about knowing when to apply algorithms and more about knowing where. There are many possible wheres. Our 3D models are born in model space. To situate models in the virtual world, their model space coordinates are transformed into world space. Many lighting algorithms are applied in camera or eye space. From […]

Goodbye, Positional Parameters

I dearly miss the year that I spent talking about shapes and math with elementary and middle school students through the lens of Madeup and 3D printing. Would that those days return! While I wait for the global health crisis to subside, I might as well fix a few bugs in Madeup—by reimplementing it without […]

Snap Circuits Bridges

We got my oldest son a Snap Circuits kit when he was very young. The product seemed like a great way to learn about electricity, but we quickly ran into the issue endemic to all educational technologies: you really need an informed human teacher to learn. We tinkered with the kit, but neither of us […]


I challenged myself to make a tulip in Twoville, and here’s my response:


I was challenged to make a raindrop in Twoville, and here’s my response: The exercise helped me fix an issue with mirror. Previously if the middle vertex was not on the mirror axis, I automatically inserted a straight line segment to bridge the gap between the mirrored segments. That produced more of a Hershey’s Kiss […]

Seven Digit Study

My son and I are on our way to school. It’s just the two of us. These drives should be a great opportunity for some genuine father-son talk, but it rarely happens. My mind is usually anxious about the day ahead, the traffic around us, and the hazards of winter. Even when we do talk, […]

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