MedicalVisualization
Edge Intersection with C++
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With C++ we use a class which encapsulates the x-,y-, and z-component of a 3D vector. The header of that vector class is part of the frame work. It represents 3D vectors as C++ object via a header-only implementation (v3d.h):
#include "v3d.h"
The vector header provides overloaded vector operators +, - and *. For example the addition of two vectors c=a+b is written as:
v3d a(1,0,0), b(0,1,0);
v3d c = a+b;
v3d c = a+b;
For that to work the +-operator is overloaded as follows:
inline v3d operator + (const v3d &a, const v3d &b)
{return(v3d(a.x+b.x, a.y+b.y, a.z+b.z));}
{return(v3d(a.x+b.x, a.y+b.y, a.z+b.z));}
With that vector class the intersection point of an iso line for the iso value v with an edge given by the endpoints x1 and x2 and the respective scalar values s1 and s2 is written as follows:
v3d x1=..., x2=...;
double s1=..., s2=...;
double w = (v-s1)/(s2-s1);
v3d p = (1-w)*x1 + w*x2;
double s1=..., s2=...;
double w = (v-s1)/(s2-s1);
v3d p = (1-w)*x1 + w*x2;
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