Diagonals of an ellipse

I have been watching Norman Wildberger’s videos on all things mathematics for about 10 years. To say that I have learned a lot is the understatement of the decade.

His most recent video is a recorded talk from July this year titled “How Chromogeometry transcends Klein’s Erlangen Program for Planar Geometries”. It is fascinating throughout but my interest was piqued when at 25:13 he starts talking about ellipses.

Continue reading “Diagonals of an ellipse”

Virtual furniture at the right scale

Our imagination is a powerful cognitive skill. When I walked into the living room of my new apartment, I experienced a rectangular empty space with a dusty concrete floor and hollow sounding acoustics. But in my mind I was already furnishing and decorating. I imagined a blue carpet on the floor, the walls lined with bookcases, a large table on the far end, and a comfortable couch near the window. Continue reading “Virtual furniture at the right scale”

Spheres in perspective

When I teach my workshop on 3D vision, the students also play with a 3D graphics framework called Scene Kit. It is very powerful and easy to use. With just a few lines of code they can create a vivid 3D scene. At some point in the tutorial, the student has created a scene with a red sphere on a grey shiny floor against a deep blue sky. Then they start playing with the controls, changing the distance, rotating the scene, or panning to the side. Invariably someone pushed the sphere to one of the corners of the image and then checks with me whether there is a mistake in the code. Continue reading “Spheres in perspective”

Detecting position and orientation of faces with iOS

4 October 2017 – I updated the code for Swift 4 and iOS 11. You can find it here.

When an iPhone is processing an image from one of its cameras, the main purpose is to make it look good for us. The iPhone has no interest in interpreting the image itself. It just wants to adjust the brightness and the colours, so that we can optimally enjoy the image.

There is however one exception. The iPhone can detect whether there is a human face in the image. It is not interested in who it is, merely that there is a face present. It can even keep track of multiple faces. Continue reading “Detecting position and orientation of faces with iOS”