Mathematics

more gears, fast

Submitted by aplesch on Wed, 11/11/2015 - 01:28

I updated the involute (curved teeth), helical gear generation procedure to use Extrusion rather than IndexedFaceSets. Extrusion automatically supports the back and front faces of the gears, and a smooth appearance by producing a mesh with points shared by triangles. So the logo code could be streamlined and therefore is now much faster generating gears.

Palm tree

Submitted by Andy on Sun, 08/11/2015 - 23:45

This is a simple design and visualisation of a palm tree. The palm leaves are borrowed from a previous blog. The new part is the tree trunk, which is an EXTRUSION object. Before the inclusion of EXTRUSION in VRMath2 Editor, tree stems or branches may be just cylinders. Using EXTRUSION, more irregular tree trunks can be achieved.

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Extrusion Star

Submitted by Andy on Sun, 08/11/2015 - 11:40

This is another test of using EXTRUSION object, perhaps a much easier test than previously on gears. In one of the Challenges, I was hoping some one can use simple geometry of pentagon to create a 3D star. It turned out EXTRUSION can achieve this quite easily.

Extrusion helical gears

Submitted by Andy on Wed, 04/11/2015 - 01:18

I recently just included Extrusion object into VRMath2 Editor and started to experiment its applications in creating 3D objects. It is quite easy to use Extrusion to create Spur Gears, but here I am showing how it can be used to created Helical Gears.

general smoothness

Submitted by aplesch on Mon, 02/11/2015 - 08:18

Getting gears to appear smooth by explicitly assigning indices to the generated facets got me thinking in more detail of how to accomplish this result in general, for any facets drawn in face mode by turtle graphics.

smoother gears

Submitted by aplesch on Fri, 30/10/2015 - 07:33

Trying to get a smoother appearance for the curved gear teeth involves lessons both in logo programming and in the underlying 3d display technology.

3d involute gears

Submitted by aplesch on Wed, 21/10/2015 - 07:30

As an update to the 2d involute (curved teeth) gears, I modified the program to produce 3d (extruded) gears. This required a change in drawing tactics.

Spur gears

Submitted by Andy on Tue, 20/10/2015 - 21:51

Finally, not perfect at all but working gear set in 3D. Thanks to asplech's blog about involute gear and this Spur Gear document, I finally get to know better about these cogged wheels.

involute gear

Submitted by aplesch on Fri, 16/10/2015 - 22:49

It turned out that producing a set of involute gears requires quite a bit of geometry in addition to involutes.

Gear 2D Prototype

Submitted by Andy on Mon, 12/10/2015 - 12:00

Following the circle involute blog, I thought about creating a gear procedure for easy creation of different gears. The method used is quite differnt to the involute idea but the turtle geometry way of thinking and doing the gears. This prototype procedure utilised a simple regular poygon formula (repeat :sides [ fd 1 rt 360/:sides ]) and some built-in commands such as TOWARD and SETHEADING to rotate the turtle and get the directions needed.

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