1. A method for generating a Cartesian mesh model of an object, comprising a processor performing the steps of:
a. receiving an ordered set of data points that describe the object in CAD-based Standard Tessellation Language (STL) format, wherein the object is described by a triangular facet surface mesh, each triangular facet having three vertices (V1, V2, V3) that uniquely define a plane and three facet edges defined by lines drawn between V1 and V2, V2 and V3, and V3 and V1;
b. defining a volume domain in Cartesian coordinates (x, y, z) that encompasses said object, said volume being subdivided into small perfect cubic cells;
c. casting ray along one of the coordinate directions originating from a cell face center of a volume domain face normal to the cast ray, to determine the intersection of said ray with said triangular facet;
d. testing ray to see if it passes through said facet by applying the orientation test for the V1V2 facet edge relative to the ray coordinates given by the determinant of the orientation test matrix for the coordinate direction of the cast ray
and similarly for the V2V3 and V3V1 facet edges; if all three orientation tests are greater than zero or all three are less than zero, proceed to step e; if only one orientation tests is zero, wherein the ray intersects an edge, or only two of the orientation tests are zero, wherein the ray intersects a vertex, then jump to step h; otherwise jump to step f;
e. saving the ray-facet intersection coordinates; proceed to f;
f. testing to see if there is another facet to test with the current ray position; if yes, jump to d and apply test to next facet; if no, proceed to g;
g. testing to see if there is a next unused cell face center in said volume domain face to cast a ray; if no proceed to step i; if yes, position ray to next cell center face and jump to step c;
h. applying a tie-breaker test to determine if the said facet is unique: (1) if said ray intersects said facet edge of a starting surface and the edge has a +x component or if the x component is zero and the facet edge has a +y component, jump to step e; if false jump to step f; (2) if said ray intersects said facet edge of an ending surface and 5 the edge has a \u2212x component or if the x component is zero and the facet edge has a \u2212y component, jump to step e; if false jump to step f; (3) if said ray intersects said facet vertex of a starting surface and both edges intersecting the vertex have +x components or if one of the x components is +x and the other zero with a +y component, jump to step e; if false jump to step f; (4) if said ray intersects said facet vertex of an ending 10 surface and both edges intersecting the vertex have \u2212x components or if one of the x components is \u2212x and the other is zero with a \u2212y component, jump to step e; if false jump to step f;
i. end ray casting.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
What is claimed is:
1. In an expandable stent, wherein said stent has a plurality of interconnected members, and wherein said interconnected members flex relative to each other as said stent expands, the improvement comprising:
an array of relief cut means formed in some of said interconnected members whereby said members flex more easily than without said relief cut means, and wherein each of said relief cut means is sufficiently small that the columnar compressive strength of said interconnected members is not significantly reduced by the presence of said relief cut means formed therein.
2. The apparatus of claim 1 wherein said stent is a balloon expandable stent.
3. The apparatus of claim 2 wherein said stent has distal and proximal ends and a central section, and wherein said relief cut means are formed only in said distal and proximal ends.
4. The apparatus of claim 2 wherein said stent has distal and proximal ends and a central section, and wherein said relief cut means are formed only in said central section.
5. The apparatus of claim 2 wherein said interconnected members of said stent have cross sections wherein the width is greater than the thickness.
6. The apparatus of claim 5 wherein said width is between 1.5 and 5 times as great as said thickness.
7. The apparatus of claim 1 wherein said relief cut means comprises one or more holes formed in and extending through one or more of said interconnecting members.
8. The apparatus of claim 7 wherein said holes are circular.
9. The apparatus of claim 7 wherein said holes are elliptical.
10. The apparatus of claim 7 wherein said holes are slots.
11. The apparatus of claim 1 wherein said stent is a self-expandable stent.
12. The apparatus of claim 1 wherein said relief cuts are applied to said stent in patterns to allow controlled, non-uniform expansion of said stent.
13. In an expandable stent having a plurality of cells and said stent is movable between a retracted and an expanded position, wherein said cells are formed by a plurality of flexible, interconnected members, said members flexing relative to each other as said tent expands, the improvement comprising:
an array of relief cut means formed in some of said members to cause said members to flex more easily than without said relief cut means being formed therein.
14. The apparatus of claim 13 wherein said stent is a balloon-expandable stent.
15. The apparatus of claim 13 wherein said interconnected members have cross sections wherein the width is between 1.5 and 5 times as great as the thickness.