Albert Chern

Assistant Professor in @ucsd_cse doing computer graphics, differential geometry, computational physics.

[Albert Chern @theAlbertChern]

Checkout our new paper #SIGGRAPH2023 involving interesting study on fluid dynamics and algebraic topology.

[Hang "Hesper" Yin @hyin2147483647]

Checkout our #SIGGRAPH2023 paper “Fluid Cohomology” 🌊🐇🍩

We show that, despite its applications, the current formulation of vorticity-streamfunction is insufficient at simulating fluids on non-simply-connected domains. [1/6]
https://t.co/OVRWsEXYqk

[Albert Chern @theAlbertChern]

There are only at most 26^60 integers that can be defined in under sixty letters. Therefore there must exist "the smallest positive integer not definable in under sixty letters" (which is a phrase with 57 letters).

[Albert Chern @theAlbertChern]

@JamesAndersonQ The differentiation of a scalar function u(A) of a matrix A is arranged as a matrix whose ij-term is the partial derivative of u(A) wrt to A_ij.

[Albert Chern @theAlbertChern]

This is neat. The gradient of the log of determinant is inverse transpose.

[Albert Chern @theAlbertChern]

For any given quadrilateral, the lines that connect the midpoints of its sides and diagonals intersect at a single point.

[Albert Chern @theAlbertChern]

If a matrix field has curl-free rows, then its cofactor matrix has div-free rows.
#ExteriorCalculusInGraphics

[Albert Chern @theAlbertChern]

Do you know how to come up with this vector identity about cofactor matrix and cross product?
(Check out our course on #ExteriorCalculusInGraphics)

[Stephanie Wang @stephamathwang]

Our #SIGGRAPH2023 course #ExteriorCalculusInGraphics is out! Learn about the fundamentals of exterior calculus and graphics related topics like geometric optimization, elasticity, and fluid dynamics in this elegant and unified language.

[Albert Chern @theAlbertChern]

For any two parabolas, the foci and all intersections of the common tangents always lie on a circle.

[Albert Chern @theAlbertChern]

@mleingang Yes they need to be 90 degrees apart for this configuration to hold.

[Albert Chern @theAlbertChern]

Consider a vertical and a horizontal parabolas sharing the same vertex. The tangents at their intersection will meet the contact points of their common tangent!

[Albert Chern @theAlbertChern]

@c_d_patterson The vertex of a parabola is that point on the parabola with maximal curvature.

[Albert Chern @theAlbertChern]

The chords of intersections from 3 (commonly oriented) parabolas always meet at a point.

[Albert Chern @theAlbertChern]

@MatthewArcus It is probably easier the other way around: Due to this concurrence of the diagonals, the hexagon has an inscribed conic (as a consequence of the converse of the Brianchon's Thm).

[Albert Chern @theAlbertChern]

For each corner of any triangle, pick an arbitrary angle and draw two rays, each apart from the adjacent edges by that angle. Then we will get a hexagon whose opposite diagonals are concurrent.

[Albert Chern @theAlbertChern]

Our #SIGGRAPH 2022 paper: Covector Fluids. With a simple modification of the advection step, a fluid solver respects the Kelvin circulation law and displays richer vortical structures.
https://t.co/NhCG2op4Ix

[sina nabizadeh @sinabiz_]

Check out our #SIGGRAPH 2022 paper: Covector Fluids 🌊🌪️
Mohammad Sina Nabizadeh
Stephanie Wang @agrograndma
Ravi Ramamoorthi
Albert Chern @theAlbertChern
https://t.co/ss8cJGydjt

[Albert Chern @theAlbertChern]

Carnot's Theorem is a generalization of the Pythagorean Theorem. The total red area equals to the total blue area.

[Albert Chern @theAlbertChern]

@gregeganSF X(389)

[Albert Chern @theAlbertChern]

For any triangle, the feet of the secondary altitudes lie on a circle.

[Albert Chern @theAlbertChern]

@gregeganSF This is called the Taylor circle. I made up the term "secondary altitude."

[Albert Chern @theAlbertChern]

From the intersection of two circles, the angle bisector of the radii meets both common tangents at a point.