Microsoft Technology Licensing, LLC

Nikola Nikolic

Oliver Michael Strunk

Maxwell Simon Abernethy

Pavle Josipovic

Eoin McLoughlin

Milan Simic

Petar Mitrovic

Rory Mullane

Milos Jovanovic

Janos Benk

Nathanael Presson

Xiao Tu

Sheng Yi

Ivan Stojiljkovic

Jelena Mojasevic

Michael Alexander Buschbeck

Alexander Sven Fichtner

David Davidovic

Norbert Nemec

Pavle Popovic

A physics engine executed on a processor to simulate real-time rigid body dynamics of a simulated physical system with a minimizing function between initial velocities and intermediate solver velocities is provided. The physics engine may be configured to iteratively loop through a collision detection phase, an iterative solving phase, updating phase, and display phase. The physics engine may be configured to store initial velocities for colliding pairs of bodies. The physics engine may be further configured to determine intermediate solver velocities for the colliding pairs of bodies based on accumulated results of constraint solving for each pair of bodies. The physics engine may be further configured to calculate friction velocities for that colliding pair of bodies based on the stored initial velocities and the intermediate solver velocities using a minimization function, and apply a friction force or impulse based on the calculated friction velocities.

Minimization function for friction solving

A physics engine executed on a processor to simulate rigid body dynamics of a simulated physical system using an inertia scaling function is provided. The physics engine may be configured to iteratively loop through a collision detection phase, an iterative solving phase, updating phase, and display phase. The physics engine may further be configured to determine a neighboring body weighting value for one or more of the plurality of bodies, and determine an inertia scaling value for the one or more of the plurality of bodies based on the neighboring body weighting value for that body. The physics engine may further be configured to scale an inertia value for a body of that colliding pair of bodies based on the inertia scaling value for the iterative solving phase.

Inertia scaling based on neighboring bodies

A computing device is provided, comprising a processor configured to execute a physics engine. The physics engine is configured to, during narrowphase collision detection of a collision detection phase, identify a set of convex polyhedron pairs, each including a first convex polyhedron from a first rigid body and a second convex polyhedron from a second rigid body. The physics engine is further configured to, for each convex polyhedron pair, determine a separating plane. The physics engine is further configured to perform neighbor welding on pair combinations of the convex polyhedron pairs during the narrowphase collision detection to thereby modify the separating planes of at least a subset of the convex polyhedron pairs. The physics engine is further configured to determine collision manifolds for the convex polyhedron pairs, including for the subset of convex polyhedron pairs having the modified separating planes.

Physics engine with collision detection neighbor welding

A computing device, including a processor configured to execute a physics engine. At a first time step, the physics engine may, for a first body located at a first position, determine a non-collision region bounded on a side by a separation plane such that when the first body is within the non-collision region, the first body does not collide with a second body. The physics engine may apply lossy compression to the separation plane to generate a compressed separation plane, and may determine a first conservative distance vector between the first body and the compressed separation plane. At a second time step, the physics engine may move the first body to a second position, determine a second conservative distance vector between the first body and the compressed separation plane, and translate the compressed separation plane based on the second position and the second conservative distance vector.

Separation plane compression

A computing device, including a processor configured to execute a physics engine. The physics engine may, for a first body having a first position and a velocity vector, determine that a second position along the velocity vector is located outside a first non-collision region for the first body and a second body. The physics engine may determine a safe position along the velocity vector at which the first body would lie tangent to a first separation plane. The physics engine may determine an advanced position along the velocity vector between the safe position and the second position, and may determine an advanced separation plane. The advanced separation plane may have an advanced normal vector based on the advanced position. The physics engine may move the first body to a new position based on the velocity vector and the advanced separation plane.

Collision detection with advanced position

Symbol recognition techniques may be applied to documents comprising various forms of content. Documents including both text and mathematical expressions may be problematic, as applying a recognizer that does not match the content may produce anomalous results. Instead, a parser may evaluate the document to classify respective regions as one of a text region or a mathematics region, based on the characteristics of each type of content. The recognizer corresponding to the content of each region may be applied to produce a composite document comprising both recognized text expressions and recognized mathematical expressions. Additional functionality may be presented based on the recognized content; e.g., text-based tools such as spell-check and natural-language translation may be applied to the text regions that comprise text expressions, and mathematics-based tools such as mathematical equation editors, mathematical expression solvers, and automated assignment grading may be applied to the mathematics regions that comprise mathematical expressions.

Evaluating documents with embedded mathematical expressions

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Belgrade, Republic of Serbia

Nikola Nikolic