The study of surface geometry is centered on the normal vector, a perpendicular direction parallel to the gradient that defines a surface's orientation and steepest ascent. This mathematical relationship is expressed through various physical properties: planes maintain a constant orientation, paraboloids have normal vectors that shift with their bowl-like curvature, and corrugated surfaces feature oscillating orientations based on trigonometric structures. To bring these concepts to life, visualization tools utilize a coordinate grid to calculate heights and render a visual skin, employing arrow-like markers for gradients and color maps to enhance depth perception. Furthermore, these static models can be converted into dynamic simulations through phase shifting, which creates the illusion of traveling waves by rapidly updating the surface's position in an animation loop.
block-beta
columns 6
CC["Criss-Cross"]:6
%% Condensed Notes
CN["Condensed Notes"]:6
RF["Relevant File"]:6
NV["Narrated Video"]:6
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") VA1("Visual Aid")MG1("Multigraph")
%% Proof and Derivation
PD["Proof and Derivation"]:6
AF("Derivation Sheet"):6
NV2["Narrated Video"]:6
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo")VA2("Visual Aid") MG2("Multigraph")
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class CC color_1
%% %% Condensed Notes
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class CN color_2
class RF color_2
classDef color_3 fill:#1e81b0,stroke:#1e81b0,color:#1e81b0
class NV color_3
class PA color_3
class AA color_3
class KT color_3
class ID color_3
class VA1 color_3
classDef color_4 fill:#47a291,stroke:#47a291,color:#47a291
class VO color_4
class MG1 color_4
%% Proof and Derivation
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class PD color_5
class AF color_5
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class NV2 color_6
class PA2 color_6
class AA2 color_6
class KT2 color_6
class ID2 color_6
class VA2 color_6
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class VO2 color_7
class MG2 color_7