Tri-cubic and hybrid interpolation in a 3D texture shader

A non-transitory computer-readable medium, on which is recorded a computer program that, when executed, performs a method for reduction of processing artifacts during three-dimensional image rendering, the method comprising:

• collecting signals after they pass through a physical object;
• generating raw volumetric data (RVD) from the collected signals, wherein the RVD is representative of the physical object;
• wherein the RVD includes a plurality of data points whose coordinates are established in a coordinate system comprising:
• an x-axis along a first dimension;
• a y-axis along a second dimension orthogonal to the first dimension;
• a z-axis along a third dimension orthogonal to the first dimension and the second dimension;
• selecting a consecutive set of data points comprising a P1, a P2, a P3, and a P4 point wherein:
• an x-axis coordinate of P1<an x-axis coordinate of P2,
• the x-axis coordinate of P2<an x-axis coordinate of P3, and
• the x-axis coordinate of P3<an x-axis coordinate of P4;
• creating a first line through P1 and P3;
• creating a first tangent vector originating at P2, parallel to the first line, and having a direction such that the projection of the first tangent vector onto the x-axis is in the direction of a projection of P3 on the x-axis;
• creating a second line through P2 and P4;
• creating a second tangent vector through P3 parallel to the second line originating at P3, and having a direction such that the projection of the second tangent vector onto the x-axis is in the direction of a projection of P2 on the x-axis;
• creating a baseline through P2 and P3;
• creating a Bezier curve between P2 and P3, wherein the Bezier curve has a degree;
• and
• determining the degree of the Bezier curve based on a comparison of the first tangent vector, the second tangent vector, and the baseline;
• and
• rendering a reduced artifact three-dimensional representation of the physical object using the Bezier curve.