1. A method for modifying data representing a geometric object, comprising: displaying a first geometric object representation dependent upon first data representing a first geometric object having a parameterization, wherein the first geometric object has a dimension greater than or equal to two, and wherein the first geometric object has an at least a two dimensional area as a pre-image in a parametric space for the parameterization; accessing respective data representing one or more additional geometric objects, wherein for each of the one or more additional geometric objects, the respective data therefor is effective for determining a boundary where the additional geometric object meets the first geometric object; wherein, for each of one or more boundaries of the above identified boundaries, a prior step of defining marker data representing at least two marker points on the boundary is performed such that for each of the marker points, there is at least one corresponding marker related extent of one of the additional geometric objects, wherein the extent is used in determining a corresponding portion of the first geometric object; for at least one of the marker points, receiving a selection by a user of the at least one of the marker point or at least one extent, as described above, for the at least one marker point; iteratively performing the following steps (A1) through (A4) so that the user perceives a substantially real time deformation of the first geometric object representation during a continuous time series of user inputs, wherein each of the user inputs is for entering a corresponding change to one of: a location for the at least one marker point, or the extent for the at least one marker point: (A1) receiving a next one of the user inputs; (A2) deriving, using the next one of the user inputs received, data representing a modified version of at least one of the additional geometric objects having the at least one marker point as one of the marker points therefor, wherein the modified version of the at least one additional geometric object includes the corresponding change, and, for the at least one additional geometric object, when: a. another of the marker points therefor, and b. the corresponding extent in the at least one additional geometric object, for the another marker point, are each not selected by the user for contributing to the real time deformation, then at least one of the another marker point, and the corresponding extent for the another marker point remains unchanged and is also included in the modified version; (A3) subsequently, determining data representing a modified instance of the first geometric object, using data representing a modified collection of the one or more additional geometric objects, wherein the modified version of the at least one additional geometric object is provided in the modified collection, wherein for each pre-image point of a plurality of points distributed throughout the two dimensional area pre-image, a corresponding substep of combining terms is performed, wherein for each object of the modified collection, one of the terms is determined by computing a product of a weighting, and data representing a particular point of the object, wherein the particular point has the pre-image point as a pre-image, and wherein for each of the pre-image points, the weightings, used in determining the terms for the corresponding substep of combining, satisfy a predetermined constraint; and (A4) displaying the modified instance of the first geometric object in accordance with the modified data representing the first geometric object.