A video demonstration of the virtual harmonograph running through a series of sixteen preset patterns. [sociallocker][/sociallocker] Read More... "Harmonograph Video Demo"
A video review of the 3-pendulum animated harmonograph model together with the tutorials (part #1, part #2). [sociallocker][/sociallocker] Read More... "A 3-pendulum Animated Harmonograph Model – video preview"
This tutorial explains a pair of important user defined functions, the “Navigator_u()” and the “Navigator_v()”. These functions save the user nine columns of formulas by calculating the effects of: 3-dimensional shift, rotations around the three axes of coordinates and 3D-2D perspective mapping. These user defined functions are also easy to use compared to writing all the perspective mapping equations from… Read More... "Instant 3D-2D Perspective Mapping – the Navigator Functions – a convenient pair of user defined functions"
The first half of this presentation dealt with mapping a 3D scene onto a 2D surface which can be a computer screen, a projection screen or the retina of the eye. By doing so we preserve much of the feel of depth of the scene. Of course when we look at an picture we get only part of the feel… Read More... "3D-2D Perspective Mapping in Excel – part #2"
In computer graphics we often need to be able to display a three-dimensional image in two dimensions and preserve the perspective appearance. If we walk on a straight road, it appears that the road narrows with the distance. This is the perspective effect and it is a result of mapping a three-dimensional image on a two-dimensional surface (i.e. a computer… Read More... "3D-2D Perspective Mapping in Excel – part #1"
Hi guys, here is the second part of a tutorial describing the matematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section describes the kinematic equations involved in the articulated linkage mechanism on the top of the table, the custom spreadsheet functions used in the model and some overall… Read More... "Modeling a Three-Pendulum Harmonograph – tutorial: part #2"
Hi guys, here is the first part of a tutorial describing the mathematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section refers only to the kinematic equations for the movement of three pendulums. A second section will be published later and it will describe the kinematic equations involved in… Read More... "Modeling a Three-Pendulum Harmonograph – tutorial: part #1"