Merge pull request #158 from alxbilger/nomenclaturemappings

Add section on mappings nomenclature

20_Simulation_Principles/50_Multi-Model_Representation/40_Mapping.md

@@ -64,6 +64,25 @@ applyDJT(const MechanicalParams*, MultiVecDerivId parentForce, ConstMultiVecDeri
 applyJT(const ConstraintParams*, MultiMatrixDerivId inConst, ConstMultiMatrixDerivId outConst );
 ```
 
+Nomenclature of Mappings
+------------------------
+
+Mappings in SOFA are designed to link two objects, enabling data transfer or interaction between them. However, some scenarios require connections where multiple objects serve as sources or targets. To handle these cases, SOFA provides specialized mapping classes that support these complex interactions:
+
+| Class         | Input                           | Output | Description                                                                                                                           |
+|---------------|---------------------------------|--------|---------------------------------------------------------------------------------------------------------------------------------------|
+| Mapping       | Single                          | Single | Standard mapping between two objects. Both objects can have different types.                                                          |
+| MultiMapping  | Multiple of the same type       | Multiple of the same type | Maps multiple input objects of the same type to multiple output objects of the same type. Types in input and output can be different. |
+| Multi2Mapping | Multiple of two different types | Multiple of the same type | Maps multiple input objects of two different types to multiple output objects of the same type.                                       |
+
+Mappings can also be categorized according to the linearity of the mapping function:
+
+| Type               | Description                                                                        |
+|--------------------|------------------------------------------------------------------------------------|
+| Linear mapping     | The Hessian tensor is null. The functions related to non-linear terms are empty.   |
+| Non-linear mapping | The Hessian tensor is not null. A geometric stiffness is generated by the mapping. |
+
+
 Common mappings
 ---------------
 - [IdentityMapping](../../../components/mapping/linear/identitymapping/) when both models have the same degrees of freedom