Abstract: A system, method, and computer program for a finding an intersection for geometrically coincident curves, comprising selecting a curve pair where at least one curve in said curve pair is a parametric curve; determining a curve parameter for each curve in said curve pair; splitting each of said curves into a plurality of candidate segments; recursively subdividing each of said candidate segments into a pair of finalized segments that are sufficiently straight; intersecting an approximation for each of said finalized segments; obtaining a plurality of next parameter values from said intersecting step; and testing for a terminating condition and appropriate means and computer-readable instructions.

Abstract: In one embodiment of a system, a computing device receives first information about a customer. To at least first and second loan sources, the computing device outputs second information enabling the first and second loan sources to determine whether to offer a loan to the customer for financing an item. The second information includes at least a portion of the first information. From the first and second loan sources, the computing device receives submissions of respective first and second offers for providing the loan to the customer for financing the item. The first and second offers are submitted by the first and second loan sources in response to the second information and in a manner that commits to provide the loan if accepted by the customer. The computing device identifies at least one of the first and second offers as being most favorable. To the customer, the computing device outputs third information about the identified offer.

Abstract: A computing device receives first information about a customer. The computing device outputs second information to at least first and second loan sources. The second information includes at least a portion of the first information. From the first and second loan sources, the computing device receives submissions of respective first and second bids for providing a loan to the customer for purchase of an item. The computing device identifies at least one of the first and second bids as being most favorable. To the customer, the computing device outputs third information about the identified bid, including an identity of at least one of the loan sources that submitted the identified bid.

Abstract: Methods and an associated apparatus for automating the funeral planning process are disclosed. Some methods involve providing a virtual funeral related transaction site to enable consumers to make selections electronically to plan a funeral without the need to visit a funeral home or interact directly with a funeral director. Some methods also involve providing a virtual funeral related transaction site to enable funeral service providers to make product selections from the offerings of suppliers where the product selections will ultimately be offered to consumers. Some methods also involve providing a predetermined set of steps that are implemented by the consumer's computer to assist the consumer in planning the funeral.