Sketch implementation

Elements-and-observables.md

@@ -34,6 +34,64 @@ Maybe being subject to a constraint can then be seen as a kind of incidence.
 
 ***To do:** Explore ideas for unifying elements and observables in spite of the contrasts described above.*
 
+## Implementation
+
+*Some thoughts on how to organize elements and observables in our code.*
+
+### Requirements
+
+#### User interface
+
+- Filter regulators by subject.
+- Look up a single-subject regulator by subject and type.
+  - When an element is the sole subject of a regulator, we'll probably want some views of the element to include a view of that regulator. For example, we might want every sphere to come with a radius regulator, with an inline radius control in a list view of the sphere.
+
+#### Engine communication
+
+- Pack element and constraint data into the format the engine uses.
+  - This requires iteration over all elements and constraints.
+
+### Structures
+
+#### Constraint problem
+
+A constraint problem description that can be passed into the engine.
+
+Fields:
+
+- Gram matrix
+- Initial configuration guess
+- Frozen entries
+
+#### Constraint satisfier
+
+A constraint problem solution that can be returned by the engine
+
+Fields:
+
+- Configuration
+- Tangent space
+
+### Traits
+
+#### Element
+
+Methods:
+
+- Write to constraint problem
+  - Representation
+  - Self-product
+- Read from constraint satisfier
+  - Representation
+
+#### Regulator
+
+- Get measurement signal
+- Get set point signal
+- Write to constraint problem
+  - Gram matrix entry (for product constraints)
+  - Index and value of frozen entry (for frozen entry constraints)
+
 ## Questions related to variables and linked constraints
 
 * Could a Scalar be an element? I.e., a "free-floating" real number?