Visual Plane
every picture states the point it is correct from
Concept

Projected not constructed — where it appears

The habit this site is built on: every point of every figure comes out of a stated camera rather than a line run to a vanishing point placed by eye. A picture no camera could produce therefore fails to build rather than appearing with nothing to say so, which is what makes the figures evidence rather than illustration.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

one pixel is an areacentrescornersprincipal point moves0.707 pxfocal length changes by4.5e-13 pxan edge-versus-centre viewport1.303 pxa half-pixel convention is a principal-point error; an off-by-one viewport is a focal-length error8 vertices, all shifted by the same 0.7071 pxspread across marks 0.0e+0 px

A pixel is not a point

Where the sample sits inside a pixel is a convention, and getting it wrong shifts every mark by half a pixel in each axis. What that costs can be measured by recovering the camera from the picture — the answer is a principal point exactly 0.707 px from the truth with the focal length untouched, and the other half-pixel mistake does precisely the reverse.

pipeline · Viewport what was drawnthe solid it depicts — reading 1 of 2xyzlooked at 45.00° off the normalcube edge 1.0000 of the drawn unitresidual 5e-16

Any three lines you draw are a cube

Four earlier essays said that cavalier projection is not the projection of anything — because its axis scales sum to three where every orthographic projection sums to two. That is true of orthographic projection and false of projection. Three lines from a point, drawn by hand, are a picture of an actual cube seen from an actual direction, and the cube and the direction come out of the drawing in closed form.

parallel · Pohlke

Named alongside it

The objects these essays reach for when they reach for this one.

DemonstrationAxonometricCamera calibrationCamera matrixDepth reversalDrawing systemFocal lengthOblique projectionOrthographicParallel projectionPlanometricPohlke

All concepts