Controlled redundancy for positioning of emitters or sensors

A system comprising an electronic processor and a non-transitory persistent memory storing instructions that, when executed by the electronic processor, determine coverage of a plurality of sensors or emitters in a physical environment by performing actions comprising:

• providing a model of the physical environment;
• positioning a respective scope of coverage shape for each sensor or emitter in the model of the physical environment, wherein a plurality of scope of coverage shapes are positioned;
• specifying a required coverage shape within the model of the physical environment;
• obtaining an indication of a required level of redundancy in coverage for the required coverage shape;
• iteratively building a graph based on the plurality of scope of coverage shapes and the required coverage shape;
• pruning the graph based at least on the required level of redundancy;
• consolidating terminal nodes of the graph to identify a part of the required coverage shape that is not covered by the plurality of sensors or emitters with the required level of redundancy;
• and
• outputting a representation of the part of the required coverage shape that is not covered by the plurality of sensors or emitters with the required level of redundancy.

A method of placing a plurality of sensors or emitters in a physical environment to achieve coverage with a specified level of redundancy, the method comprising:

• providing a model of the physical environment;
• positioning a respective scope of coverage shape for each sensor or emitter in the model of the physical environment, wherein a plurality of scope of coverage shapes are positioned, wherein each of the plurality of scope of coverage shapes are represented in the computer using one of:
• vector representation, parametric curve representation, parametric surface representation, analytical equation representation, polygon parameterization, or polyhedron parameterization;
• specifying a required coverage shape within the model of the physical environment, wherein the required coverage shape is represented in the computer using one of:
• vector representation, parametric curve representation, parametric surface representation, analytical equation representation, polygon parameterization, or polyhedron parameterization;
• obtaining an indication of a required level of redundancy in coverage for the required coverage shape;
• iteratively building a binary tree, wherein the iteratively building comprises adding additional levels in the binary tree by, for each parent node in a previous level of the binary tree,
• adding a first child node that represents a set represented by the parent node intersected with a scope of coverage shape of the plurality of scope of coverage shapes, and
• adding a second child node that represents a set represented by the parent node subsequent to set subtraction by a scope of coverage shape of the plurality of scope of coverage shapes;
• pruning the binary tree based at least on the required level of redundancy;
• consolidating terminal nodes of the binary tree to identify a part of the required coverage shape that is not covered by the plurality of sensors or emitters with the required level of redundancy;
• outputting a representation of the part of the required coverage shape that is not covered by the plurality of sensors or emitters with the required level of redundancy;
• and
• arranging the sensors or emitters in the physical environment based on the outputting.