Creates a new PointedPillar geometry.
Configuration options.
Protected_Cached bounding volume to prevent re-allocation
Protected_The indices of the geometry for indexed rendering.
Protected_Whether the geometry is purely line-based.
Protected Optional_Optional skinning joints (4 IDs per vertex).
Protected_The normals of the geometry (nx, ny, nz).
Protected_The tangents of the geometry (tx, ty, tz).
Protected_The UV coordinates of the geometry (u, v).
Protected_The vertices of the geometry (x, y, z).
Protected Optional_Optional skinning weights (4 weights per vertex).
Protected_The indices for wireframe rendering.
Height of the lower column shaft (h1).
Number of height subdivisions on column shaft.
Height of the conical roof tip (h2).
Whether the bottom base is open.
Number of radial subdivisions.
Radius at the bottom base (a).
Radius at the transition ring (b).
Central angle in radians.
Start angle in radians.
Protected_Helper method to create an appropriately sized index array. Automatically chooses between 16-bit and 32-bit indices based on vertex count.
The number of indices needed.
A Uint16Array or Uint32Array.
Applies a Matrix4 transformation to all geometry vertices in-place.
The transformation matrix.
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Computes the normals of the geometry using the current vertices and indices. Averages normals for shared vertices.
Computes the tangents of the geometry based on normals and UVs. Required for normal mapping.
Computes the wireframe indices (line-segments) from the current triangle topology.
ProtectedgenerateGenerates the raw geometry data. Must be implemented by subclasses.
Calculates the bottom base circular area $A_{\text{base}} = \pi a^2$.
Returns a bounding volume that encapsulates this geometry.
The bounding volume.
Returns the raw geometry data ready for GPU upload.
The geometry data interface.
Calculates the lateral mantle area (column mantle + tip mantle).
Calculates the slant height of the lower column $s_1 = \sqrt{(a - b)^2 + h_1^2}$.
Calculates the slant height of the conical tip $s_2 = \sqrt{b^2 + h_2^2}$.
Calculates the total surface area $A = A_{\text{base}} + M$.
Calculates the volume $V = \frac{\pi}{3} \left( h_1(a^2 + ab + b^2) + b^2 h_2 \right)$.
Rotates the geometry vertices around the X-axis in-place.
The rotation angle in radians.
this
Rotates the geometry vertices around the Y-axis in-place.
The rotation angle in radians.
this
Rotates the geometry vertices around the Z-axis in-place.
The rotation angle in radians.
this
Scales the geometry vertices in-place.
The scale factor.
this
A pointed pillar geometry (Spitze Säule / obelisk-like column with conical tip).
Consists of a lower frustum column of height $h_1$ tapering from base radius $a$ to transition radius $b$, topped by a conical tip of height $h_2$ with base radius $b$.
Mathematical formulas:
See
https://rechneronline.de/pi/spitze-saeule.php