Compare LinearSolve result x with Eigen (RobotLocomotion#16045)

Compare LinearSolve result with calling Eigen's solve result.
Co-authored-by: rpoyner-tri

[geometry] Add MeshcatCone isa Shape (RobotLocomotion#15936)

* [geometry] Add MeshcatCone isa Shape

This supports visualizing cone geometries in meshcat (which is
immediately useful for drawing the arrowheads of contact force
vectors).

Per a discussion with @SeanCurtis-TRI, we've decided to add the type
to the main Shape class hierarchy, but with a class name
(`MeshcatCone`) that makes it obvious that the current support for
this shape is limited to Meshcat.

[geometry:meshcat] Add UI controls to Meshcat (RobotLocomotion#15768)

* [geometry:meshcat] Add UI controls to Meshcat

Adds support for buttons and sliders inside the meshcat browser.  This
is also the first instance of a bidirectional communication (the new
direction being browser => c++).  I've been using it for class for a
week or so, and it's been working well under that stress test.

Breaking change: Fixed a spelling error in the MeshcatVisualizerParams
field:
delete_on_intiliazation_event => delete_on_initialization_event.

Makes ValidateCreatedForThisSystem() inline-able and moves it to Syst…

…emBase (RobotLocomotion#15595)

[fem] Move quadrature classes out of dev (RobotLocomotion#15334)

* [fem] Move quadrature classes out of dev

Along with the file moving:

* Move the quadrature classes to internal:: namespace.
* Change template integral constant names to be style-guide compliant.
* Clean up unit test.

parsing: Remove implicit frames created for nested models. (RobotLoco…

…motion#15208)

This removes additional implicit model frames created for nested models that were missed in RobotLocomotion#15099.

Remove deprecated code 2021-04-21 (RobotLocomotion#15050)

Missed previously, perhaps owing to idiosyncratic date.

* drake::multibody::MultiBodyPlant::CalcCenterOfMassPosition
  * all overloads

pydrake: Replace "System YAML" with proper ".. pydrake_system::" dire…

…ctive (RobotLocomotion#14915)

* pydrake: Replace "System YAML" with proper ".. pydrake_system::" directive

Add script for building drake-visualizer on macOS (RobotLocomotion#14771

)

[FEM] Implement CorotatedModel and math helpers (RobotLocomotion#14599)

* Implement CorotatedModel and math helpers.

- Implement the fixed corotated model from Stomakhin, Alexey, et al.
 "Energetically consistent  invertible elasticity." Proceedings of the
 11th ACM SIGGRAPH/Eurographics conference on Computer Animation. 2012.

- Implement a few matrix calculation helpers to facilitate
 CorotatedModel.

- Refactor utility functions for St-Venant type constitutive models
 into free functions.

- Refactor LinearConstitutiveModelTest to test for both
 LinearConstitutiveModel and CorotatedModel.