Here is a mesh I computed in order to evoke the new Gridcoin logo https://steemitimages.com/0x0/http://i.imgur.com/0UPGfqI.png (thanks @joshoeah). First, I decomposed the logo into elementary shapes like lines, circles and meeting points. Then I computed the distance function to the global shape defined as the minimum of all the distances from those elementary shapes. Then I ran a mesher which adapts to the metrics defined by that function. Et voilà! https://upload.wikimedia.org/wikipedia/commons/4/4b/GridcoinMesh.png By Zipity.grc (Own work) [<a href="https://creativecommons.org/licenses/by-sa/4.0">CC BY-SA 4.0</a>], <a href="https://commons.wikimedia.org/wiki/File%3AGridcoinMesh.png">via Wikimedia Commons</a> The hardest part (beside writing the mesher) was to tweak half a dozen of coefficients in order to stress the 'active' locations -- the shape itself -- from the backgound by varying triangle density. The result has T = 7202 triangles, and as you can count there are B = 12 border edges (and 12 border vertices obviously). Fun fact : this is enough to compute E the total number of edges! Indeed, as <center> <a href="https://www.codecogs.com/eqnedit.php?latex=2E-3T=B" target="_blank"><img src="https://latex.codecogs.com/gif.latex?2E-3T=B" title="2E-3T=B" /></a></center> for any triangular mesh, we have E = 10809 edges. And now, since the Euler characteristic is 1 for a planar mesh <center> <a href="https://www.codecogs.com/eqnedit.php?latex=V-E+T=1" target="_blank"><img src="https://latex.codecogs.com/gif.latex?V-E+T=1" title="V-E+T=1" /></a></center> so V = 3608 vertices. (edit: hints for a proof [here](https://steemit.com/mathematics/@zipity/the-dehn-sommerville-equations))
author | zipity |
---|---|
permlink | adaptative-mesh-applied-to-the-gridcoin-logo |
category | art |
json_metadata | {"tags":["art","mathematics","simplex","steemstem","gridcoin"],"users":["joshoeah"],"image":["https://steemitimages.com/0x0/http://i.imgur.com/0UPGfqI.png","https://upload.wikimedia.org/wikipedia/commons/4/4b/GridcoinMesh.png","https://latex.codecogs.com/gif.latex?2E-3T=B","https://latex.codecogs.com/gif.latex?V-E+T=1"],"links":["https://creativecommons.org/licenses/by-sa/4.0","https://commons.wikimedia.org/wiki/File%3AGridcoinMesh.png","https://www.codecogs.com/eqnedit.php?latex=2E-3T=B","https://www.codecogs.com/eqnedit.php?latex=V-E+T=1","https://steemit.com/mathematics/@zipity/the-dehn-sommerville-equations"],"app":"steemit/0.1","format":"markdown"} |
created | 2018-01-11 15:04:12 |
last_update | 2018-12-04 16:03:39 |
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children | 11 |
last_payout | 2018-01-18 15:04:12 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 11.968 HBD |
curator_payout_value | 3.594 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 1,712 |
author_reputation | 149,205,932,410 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,775,775 |
net_rshares | 1,956,124,312,057 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
vortac | 0 | 1,687,144,900,746 | 43% | ||
warofcraft | 0 | 0 | 20% | ||
barton26 | 0 | 4,513,289,733 | 100% | ||
darth-cryptic | 0 | 7,635,040,614 | 100% | ||
sodom | 0 | 1,648,436,631 | 100% | ||
nuad01 | 0 | 669,310,744 | 100% | ||
grider123 | 0 | 6,466,513,813 | 100% | ||
jringo | 0 | 17,345,541,143 | 50% | ||
joshoeah | 0 | 5,280,428,511 | 100% | ||
zipity | 0 | 818,959,863 | 100% | ||
rufflebene | 0 | 0 | 100% | ||
thorondor | 0 | 781,983,745 | 100% | ||
pahom | 0 | 614,860,000 | 100% | ||
applepiie | 0 | 1,318,450,346 | 100% | ||
parejan | 0 | 16,008,115,746 | 100% | ||
jefpatat | 0 | 11,941,326,341 | 100% | ||
steemmillionaire | 0 | 14,186,655,967 | 100% | ||
alanman | 0 | 5,388,013,124 | 100% | ||
zoyabbrag | 0 | 53,521,085 | 100% | ||
bakhr | 0 | 62,334,734 | 100% | ||
gregan | 0 | 5,134,411,349 | 100% | ||
hotbit | 0 | 21,963,849,774 | 100% | ||
geebell | 0 | 4,080,327,721 | 100% | ||
ivanviso | 0 | 418,639,913 | 100% | ||
donkeykong9000 | 0 | 138,758,670,227 | 100% | ||
igorlik13 | 0 | 606,090,200 | 100% | ||
wisecracka | 0 | 463,980,748 | 100% | ||
h202 | 0 | 2,311,329,304 | 100% | ||
alexmaksto | 0 | 509,329,935 | 100% |
Instead of trying to understand it i'll just gaze in awe.. 😵
author | gregan |
---|---|
permlink | re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180113t093010005z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-13 09:30:12 |
last_update | 2018-01-13 09:30:12 |
depth | 1 |
children | 0 |
last_payout | 2018-01-20 09:30:12 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.000 HBD |
curator_payout_value | 0.000 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 68 |
author_reputation | 8,998,388,809,667 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 29,190,784 |
net_rshares | 753,617,321 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
zipity | 0 | 753,617,321 | 100% |
author | h202 |
---|---|
permlink | re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t183013756z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 18:30:15 |
last_update | 2018-01-11 18:30:15 |
depth | 1 |
children | 2 |
last_payout | 2018-01-18 18:30:15 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.036 HBD |
curator_payout_value | 0.004 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 41 |
author_reputation | 260,059,645,359 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,818,084 |
net_rshares | 5,824,235,995 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
zipity | 0 | 775,398,168 | 100% | ||
gregan | 0 | 5,048,837,827 | 100% |
Physics rule! Would you help me run some fluid simulation on this ?
author | zipity |
---|---|
permlink | re-h202-re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t192052007z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 19:20:51 |
last_update | 2018-01-11 19:20:51 |
depth | 2 |
children | 1 |
last_payout | 2018-01-18 19:20:51 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.000 HBD |
curator_payout_value | 0.000 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 67 |
author_reputation | 149,205,932,410 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,827,484 |
net_rshares | 2,311,329,304 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
h202 | 0 | 2,311,329,304 | 100% |
Perhaps, but I'm not a fluid dynamicist :P Not sure how much work that would involve. Maybe there are some existing packages out there that can simulate Navier-Stokes on a custom mesh. Not the kind of thing I'd want to code from scratch..!
author | h202 |
---|---|
permlink | re-zipity-re-h202-re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t220717497z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 22:07:18 |
last_update | 2018-01-11 22:07:18 |
depth | 3 |
children | 0 |
last_payout | 2018-01-18 22:07:18 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.000 HBD |
curator_payout_value | 0.000 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 239 |
author_reputation | 260,059,645,359 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,856,148 |
net_rshares | 0 |
I don't understand a bit of it but it sounds scientific ;-)
author | jefpatat |
---|---|
permlink | re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t180748659z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 18:07:48 |
last_update | 2018-01-11 18:07:48 |
depth | 1 |
children | 1 |
last_payout | 2018-01-18 18:07:48 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.000 HBD |
curator_payout_value | 0.000 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 59 |
author_reputation | 26,609,526,234,408 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,813,913 |
net_rshares | 805,891,354 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
zipity | 0 | 805,891,354 | 100% |
Lol ! Metrics is like the scale on a map. Except it is not written once on the map, it is defined differently for every point on the map . This kind of mesh is just a series of equilateral triangles, except they are drawn with respect to a special metrics : the metrics (the scale) which zooms according to the distance to the shape of the logo. I hope I could give the general idea :/
author | zipity |
---|---|
permlink | re-jefpatat-re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t183005547z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 18:30:06 |
last_update | 2018-01-11 18:30:06 |
depth | 2 |
children | 0 |
last_payout | 2018-01-18 18:30:06 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.000 HBD |
curator_payout_value | 0.000 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 386 |
author_reputation | 149,205,932,410 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,818,057 |
net_rshares | 0 |
Nice work! I have no idea how you achieved this - anything mathematics goes way over my head :) - so this is like some kind of wizardry to me! Is the final result capable of being exported in a vector format? It might be fun to play around with for interesting artistic applications :)
author | joshoeah |
---|---|
permlink | re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t152155488z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 15:22:06 |
last_update | 2018-01-11 15:22:06 |
depth | 1 |
children | 4 |
last_payout | 2018-01-18 15:22:06 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.120 HBD |
curator_payout_value | 0.004 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 286 |
author_reputation | 564,475,220,249 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,779,954 |
net_rshares | 16,038,528,145 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
sodom | 0 | 1,614,564,646 | 100% | ||
grider123 | 0 | 6,359,629,288 | 100% | ||
jringo | 0 | 6,861,972,320 | 20% | ||
zipity | 0 | 792,822,846 | 100% | ||
ivanviso | 0 | 409,539,045 | 100% |
Thanks @joshoeah! You can't say your logo has nothing mathematical in it! Lines and circles, that's all there is ;-) About the format, as a matter of fact I used an SVG version for producing the png. <a href=http://svgshare.com/i/4uX.svg>Here</a> it is . By the way, this is @originalworks Speaking of applications, the inital use of a mesh is to simulate fluid dynamics equations on it. I'm thinking of a gif where the logo moves like a liquid or a fire.
author | zipity |
---|---|
permlink | re-joshoeah-re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t161607460z |
category | art |
json_metadata | {"tags":["art"],"users":["joshoeah","originalworks"],"links":["http://svgshare.com/i/4uX.svg"],"app":"steemit/0.1"} |
created | 2018-01-11 16:16:09 |
last_update | 2018-01-11 16:27:51 |
depth | 2 |
children | 3 |
last_payout | 2018-01-18 16:16:09 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.070 HBD |
curator_payout_value | 0.016 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 458 |
author_reputation | 149,205,932,410 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,791,452 |
net_rshares | 11,586,910,815 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
grider123 | 0 | 6,450,355,270 | 100% | ||
joshoeah | 0 | 5,136,555,545 | 100% |
Wow fluid dynamics with this image sounds incredible cool! Would love to see this.
author | grider123 |
---|---|
permlink | re-zipity-re-joshoeah-re-zipity-adaptative-mesh-applied-to-the-gridcoin-logo-20180111t193411003z |
category | art |
json_metadata | {"tags":["art"],"app":"steemit/0.1"} |
created | 2018-01-11 19:34:12 |
last_update | 2018-01-11 19:34:12 |
depth | 3 |
children | 2 |
last_payout | 2018-01-18 19:34:12 |
cashout_time | 1969-12-31 23:59:59 |
total_payout_value | 0.036 HBD |
curator_payout_value | 0.004 HBD |
pending_payout_value | 0.000 HBD |
promoted | 0.000 HBD |
body_length | 82 |
author_reputation | 107,965,352,035,530 |
root_title | "Adaptative mesh applied to the Gridcoin logo" |
beneficiaries | [] |
max_accepted_payout | 1,000,000.000 HBD |
percent_hbd | 10,000 |
post_id | 28,829,911 |
net_rshares | 5,705,598,168 |
author_curate_reward | "" |
voter | weight | wgt% | rshares | pct | time |
---|---|---|---|---|---|
joshoeah | 0 | 4,934,556,169 | 100% | ||
zipity | 0 | 771,041,999 | 100% |