Generating surface approximations using curvature integrals for surface visualization rendering

An apparatus comprising at least one processor, at least one non-transitory memory storing computer program code, and at least one communications interface configured to communicate via at least one network, the computer program code configured to, when executed by the at least one processor, cause the apparatus to at least:

• access terrain data describing a surface, the terrain data comprising a plurality of positions, each position of the plurality of positions comprises a location and a height, wherein the terrain data comprises (a) a first position comprising a first location and a first height and (b) a second position comprising a second location and a second height;
• determine curvatures of the surface between adjacent positions along the surface, wherein a first curvature between the first position and the second position is a second derivative of a connecting line between the first position and the second position, wherein the plurality of positions comprises multiple positions located on a surface spanning line that is collinear with the connecting line;
• define one or more vertices, wherein a vertex of the one or more vertices is defined by:
• determine an accumulated absolute curvature along a portion of the surface spanning line based on the curvature between points of one or more of the plurality of data points by adding the absolute value of the first curvature to the accumulated absolute curvature,
• determine whether the accumulated absolute curvature is equal to or greater than a reset value,
• when it is determined that the accumulated absolute curvature is equal to or greater than the reset value, define a vertex at the second position, and
• when it is determined that the accumulated absolute curvature is not equal to or greater than the reset value, add an absolute value of a second curvature to the accumulated absolute curvature, wherein the second curvature is a second derivative of a connecting line defined by the second position and a third position of the plurality of positions, the third position located on the surface spanning line;
• and
• provide the one or more vertices for use in defining a surface mesh, wherein the surface mesh represents the surface and is configured for use in rendering a visualization of the surface via a user interface and/or performing a navigation function.

A computer program product comprising at least one non-transitory computer-readable storage medium having computer-executable program code instructions stored therein, the computer-executable program code instructions comprising program code instructions configured to, when executed by a processor of an apparatus, cause the apparatus to at least:

• access terrain data describing a surface, the terrain data comprising a plurality of positions, each position of the plurality of positions comprises a location and a height, wherein the terrain data comprises (a) a first position comprising a first location and a first height and (b) a second position comprising a second location and a second height;
• determine curvatures of the surface between adjacent positions along the surface, wherein a first curvature between the first position and the second position is a second derivative of a connecting line between the first position and the second position, wherein the plurality of positions comprises multiple positions located on a surface spanning line that is collinear with the connecting line;
• define one or more vertices, wherein a vertex of the one or more vertices is defined by:
• determine an accumulated absolute curvature along a portion of the surface spanning line based on the curvature between points of one or more of the plurality of data points by adding the absolute value of the first curvature to the accumulated absolute curvature,
• determine whether the accumulated absolute curvature is equal to or greater than a reset value,
• when it is determined that the accumulated absolute curvature is equal to or greater than the reset value, define a vertex at the second position, and
• when it is determined that the accumulated absolute curvature is not equal to or greater than the reset value, add an absolute value of a second curvature to the accumulated absolute curvature, wherein the second curvature is a second derivative of a connecting line defined by the second position and a third position of the plurality of positions, the third position located on the surface spanning line;
• and
• provide the one or more vertices for use in defining a surface mesh, wherein the surface mesh represents the surface and is configured for use in rendering a visualization of the surface via a user interface and/or performing a navigation function.