{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-9818223","patent":{"patent_number":"US-9818223","title":"Method of forming a freeform surface shaped element for an illumination system","assignee":null,"inventors":[],"filing_date":"2015-05-12T00:00:00.000Z","publication_date":"2017-11-14T00:00:00.000Z","cpc_codes":["G06T","G06F"],"num_claims":8,"abstract":"A construction method of freeform surface shape based on XY-polynomial obtains a plurality of data points of a freeform surface according to an object point and an imaging point in a three-dimensional Cartesian coordinates system Oxyz. Each of the plurality of data points comprises a coordinate value Qi and a normal vector Ni. A first sum of squares e1(P) of coordinate differences in z direction between the coordinate value Qi and the freeform surface is applied, and by a second sum of squares e2(P) between the normal vector Ni of the data points and a normal vector ni of the freeform surface, a modulus of vector differences is acquired. An evaluation function ƒ(p)=e1(P)+we2(P) is proposed and a plurality of freeform surface shapes obtained by selecting and applying different weightings. A final freeform surface shape Ωopt is chosen from the plurality of freeform surface shapes."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Method of forming a freeform surface shaped element for an illumination system","description":"A construction method of freeform surface shape based on XY-polynomial obtains a plurality of data points of a freeform surface according to an object point and an imaging point in a three-dimensional","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-9818223","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-9818223","citation_suggestion":"Patentable. \"Method of forming a freeform surface shaped element for an illumination system\" (US-9818223). https://patentable.app/patents/US-9818223","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-9818223","json":"https://patentable.app/api/llm-context/US-9818223","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-06-06T07:28:05.440Z"}