Interactive General Quadric Surface with Adjustable Parameters

This example demonstrates how to explore the general quadric surface equation ax²+by²+cz²+dxy+eyz+fzx+gx+hy+iz+j=0 by adjusting all ten coefficients via sliders, allowing real-time visualization of the resulting 3D surface. The core mathematical concepts include classification of quadric surfaces (ellipsoids, hyperboloids, paraboloids, cones) and the intersection curves obtained by slicing the surface with planes. Construction highlights: GeoGebra commands such as Plane, IntersectPath, and SelectedIndex are used to create slicing planes (zSlice, xSlice, ySlice) and compute their intersection paths with the surface. Objects include coefficient sliders (ax2, ay2, az2, axy, ayz, azx, ax, ay, az, a0) and slice-related objects (xySliceEq, yzSliceEq, zxSliceEq, text3D, etc.). This is suitable for high school or undergraduate courses in analytic geometry, solid geometry, or mathematical experimentation, helping students intuitively grasp how parameters affect surface shape and cross-sections.