Group Assignment 3
Laplacian Meshes

In this assignment, groups implemented a differential representation of a surface mesh known as the Laplacian Mesh representation. This enabled a variety of applications, such as dragging points to make the mesh deform nonrigidly ("Laplacian mesh editing"), interpolating functions across surfaces, geometry filtering, mesh flattening, heat flow, and curvature estimation.

Results are below. Student analysis from their README files is provided in quotes where appropriate


Cotangent vs Umbrella Weights



Homer Spectral Modes




Cheetah Lowpass 20 Eigenvectors

Looks quite malnourished...

John/Natalie/Zach (Winners!!)

Sharpened Cheetah

"He's been lifting a lot"

Threatening Lowpass Dragon

Lowpass Teapot

Disembodied Checkered Homer

Dressing Homer

Goal image found at

Argentine Soccer Homer

Walking Homer

Brandon/Nina/Cosi (Runners Up)

Cheetah Heat Flow

Colors Dragon

Flattening Teapot


Homer Blooper

Lowpass Homer

Man Flames

Striped Cow

Chalena/Ba'Carri (Runners Up)

Bird Flapping

Anchor SelectionUmbrella WeightsCotangent Weights
"This makes sense considering what was said during class about the cotangent weights using angles, thus leading to better preservation during deformation and a visually smoother result."

Hot Dragon

Blooper Colored

Flattened Teapot

Chris's Face Checkerboard

"We decided to do texture mapping using the default chessboard on Chris's face... Coincidentally this might be a good makeup idea for next Halloween"


Dragon Flattened

Homer Smoothing Bloopers

Teapot Laplacian Smoothed 3x

Teapot Minimal Surface

"The minimal surface preserves the topology of handle when six anchors are set in the teapot mesh"


"We submitted funny or scary/unsetttling results discovered during testing"

"Homer Creepy AF Blooper"

"Homer Umbrella 2"

"Short Homer Blooper"

"Squashed Homer Blooper"


Stubby Homer

"This was a mesh which we encountered while implementing cotangent weights. It occurs when we pick anchors to raise Homer's arms and stationary points on Homer's chest and face, but not on Homer's feet. Cotangent weights on this configuration squeezes Homer. I thought this was a bug for the longest time, but its actually not. Good learning experience."


Disco Homer!

Angry Cold Hands Homer (Laplacian Eigen Mode Number 5)

Bird Checkerboard


Lowpass Homer 300 Eigenvectors

Heat Flow Homer Fingers


Cheetah Lowpass 50 Eigenvectors

"It has no face!"

Denoised Homer 666 Eigenvectors

Noisy Homer BeforeLowpass Filtered 666 Eigenvectors


Smooth Cow

Lowpass Homer, 20 Eigenvectors

Cheetah Colored

Bird Colored

Annie / Mingyuan

Heat Flow Homer

Lowpass Homer

Lowpass Teapot