Spatial queries

Apparatus comprising:

• a) at least one graphics processing unit (GPU);
• and
• b) a non-transitory computer readable medium storing instructions which, when executed by the at least one GPU, cause the at least one GPU to perform a method for performing a spatial query, the method including
• 1) Receiving spatial data as a first input,
• 2) Receiving a spatial query parameter as a second input,
• 3) embedding geometry of the first input onto a first set of at least one planar canvas, each of which corresponds to one or more geometric objects, wherein the act of embedding a geometric object of the first input onto a first planar canvas includes (1) defining a first set of canvas points on the first planar canvas where its corresponding geometric object intersects, and (2) associating each of the canvas points of the first set with an identifier and at least one attribute value,
• 4) Embedding geometry of the second input onto a second set of at least one planar canvas, each of which corresponds to one or more geometric objects, wherein the act of embedding a geometric object of the second input onto a second planar canvas includes (1) defining a second set of canvas points on the second planar canvas where its corresponding geometric object intersects, and (2) associating each of the canvas points of the second set with an identifier and at least one attribute value, and
• 5) Performing any combination of at least one geometric operations, on the first set of at least one planar canvas and the second set of at least one planar canvas to generate at least one output planar canvas,
• wherein each of the canvas points of the first set and the second set is associated with a matrix or array including one of a geometric point, polyline, or polygon identifier, and one or more attribute values used by the at least one geometric operations.

Apparatus comprising:

• a) at least one graphics processing unit (GPU);
• and
• b) a non-transitory computer readable medium storing instructions which, when executed by the at least one GPU, cause the at least one GPU to perform a method for performing a spatial query, the method including:
• 1) Receiving as a first input, a first set of at least one planar canvas embedding geometry of spatial data, wherein each of the at least one planar canvas of the first set includes a set of canvas points on the planar canvas where its corresponding geometric object intersects, each of which canvas points being associated with both (i) an identifier and (ii) a matrix or array including one of a geometric point, polyline, or polygon identifier, and one or more attribute values,
• 2) Receiving a spatial query parameter as a second input,
• 3) Embedding geometries of the second input onto a second set of at least one planar canvas, wherein the act of embedding a geometric object of the second input onto a second planar canvas includes (1) defining a second set of canvas points on the second planar canvas where its corresponding geometric object intersects, and (2) associating each of the canvas points of the second set with an identifier and at least one attribute value, and
• 4) Performing any combination of at least one operation on the first set of at least one planar canvas and the second set of at least one planar canvas to generate one or more output planar canvases,
• wherein the spatial query parameter is a set of one or more geometric objects, and each of the geometric objects is a combination of one or more of (A) a geometric point, (B) a polyline, or (C) a polygon, and
• wherein each of the canvas points of the second set is associated with a matrix or array including one of a geometric point, polyline, or polygon identifier, and one or more attribute values used by the at least one operation.

Apparatus comprising:

• a) at least one graphics processing unit (GPU);
• and
• b) a non-transitory computer readable medium storing instructions which, when executed by the at least one GPU, cause the at least one GPU to perform a GPU implemented method for converting first spatial data having a corresponding first geometric object into a first planar canvas and converting second spatial data having a corresponding second geometric object into a second planar canvas, the GPU implemented method including
• 1) Receiving as input, the first and second spatial data, and
• 2) Embedding geometry of the first spatial data onto the first planar canvas by (1) defining a first set of canvas points on the first planar canvas where the geometric object intersects, and (2) associating each of the canvas points of the first set with an identifier and at least one attribute value, wherein the act of embedding a geometric object of the input onto the first planar canvas includes (1) defining the first set of canvas points on the first planar canvas where its corresponding geometric object intersects, and (2) associating each of the canvas points of the first set with an identifier and at least one attribute value, wherein the act of embedding the second geometric object of the input onto the second planar canvas includes (1) defining a second set of canvas points on the second planar canvas where its corresponding geometric object intersects, and (2) associating each of the canvas points of the second set with an identifier and at least one attribute value, and wherein each of the canvas points of the first set and the second set is associated with a matrix or array including one of a geometric point, polyline, or polygon identifier, and one or more attribute values used by the at least one geometric operation.