Quadric Surfaces Demo by Muhammad Zia Afzal

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2019-03-12 02:39

This example demonstrates the 3D visualization of quadric surfaces under varying parameters. It involves core math concepts like quadric surface equations, 3D coordinate transformations, and parametric representation. Construction highlights include commands like SelectedIndex, If, and IntersectPath, along with objects such as Quadrics, Sliders, and Loci. Ideal for high school students and math enthusiasts studying spatial geometry and calculus.

GeoGebra Commands & Parameters

SelectedIndex(axesofquad) → aoq
SelectedIndex(Quadrics) → quad
SelectedIndex(traces) → traces_1
If(traces_1 ≟ 1, x + (0 * z) = k, traces_1 ≟ 2, y + (0 * z) = k, traces_1 ≟ 3, z = k) → tracesinplane
If(quad ≟ 1, x^(2) / a^(2) + y^(2) / b^(2) + z^(2) / c^(2) = 1, quad ≟ 3 ∧ aoq ≟ 2, ((-x^(2))) / a^(2) + y^(2) / b^(2) - z^(2) / c^(2) = 1, quad ≟ 3 ∧ aoq ≟ 3, ((-x^(2))) / a^(2) - y^(2) / b^(2) + z^(2) / c^(2) = 1, quad ≟ 4 ∧ aoq ≟ 1, x^(2) = y^(2) / b^(2) + z^(2) / c^(2), quad ≟ 4 ∧ aoq ≟ 2, y^(2) = z^(2) / c^(2) + x^(2) / a^(2), quad ≟ 4 ∧ aoq ≟ 3, z^(2) = x^(2) / a^(2) + y^(2) / b^(2), quad ≟ 2 ∧ aoq ≟ 1, quad ≟ 5 ∧ aoq ≟ 1, x = y^(2) / b^(2) + z^(2) / c^(2), quad ≟ 5 ∧ aoq ≟ 2, y = z^(2) / c^(2) + x^(2) / a^(2), quad ≟ 5 ∧ aoq ≟ 3, z = x^(2) / a^(2) + y^(2) / b^(2), quad ≟ 6 ∧ aoq ≟ 1, x = y^(2) / b^(2) - z^(2) / c^(2), quad ≟ 6 ∧ aoq ≟ 2, y = z^(2) / c^(2) - x^(2) / a^(2), ((-x^(2))) / a^(2) + y^(2) / b^(2) + z^(2) / c^(2) = 1, quad ≟ 6 ∧ aoq ≟ 3, z = x^(2) / a^(2) - y^(2) / b^(2), quad ≟ 2 ∧ aoq ≟ 2, x^(2) / a^(2) - y^(2) / b^(2) + z^(2) / c^(2) = 1, quad ≟ 2 ∧ aoq ≟ 3, x^(2) / a^(2) + y^(2) / b^(2) - z^(2) / c^(2) = 1, quad ≟ 3 ∧ aoq ≟ 1, x^(2) / a^(2) - y^(2) / b^(2) - z^(2) / c^(2) = 1) → qsurf
IntersectPath(tracesinplane, qsurf) → d
SelectedIndex(colorobj) → colorobjind
SelectedIndex(colorobj) → l