The orthogonal projection of a vector onto a line passing through the origin
Author: shiroeExecutions: 24
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This calculates the orthogonal projection of a vector.
| θ | rad |
| The value of (θ/2π)*360 | |
| Ts11 | Ts12 |
| Ts21 | Ts22 (The numbers to the right of the letters indicate row and column numbers) |
| bx | (The x-component of vector b after orthogonal projection) |
| by | (The y-component of vector b after orthogonal projection) |
| m_nx | (Unit vector in the direction of a line—x-component) |
| m_ny | (Unit vector in the direction of a line—y-component) |
| n_ax | (Unit vector of vector a: x-component) |
| n_ay | (Unit vector of vector a: y-component) |
| L | (Length of an orthogonally projected vector) |
This is a linear transformation. Consider the xy-plane.
We perform an orthogonal projection of vector a—whose initial point is fixed at the origin—onto a line passing through the origin.
The initial point of the projected vector b is also the origin, and its terminal point lies at the point where a perpendicular line is dropped from the terminal point of a to the line.
Its length is equal to the norm of a multiplied by cosθ (where the angle is positive when measured counterclockwise).
The angle θ is determined by the value of the inverse tangent function with respect to the slope m of the line.
Therefore, we assume 0 < |m| < ∞ (-π/4 < θ < π/4).
Thus, θ is not the azimuth of the line’s direction unit vector itself. It is a numerical value used to determine the matrix element Ts
of the orthogonal projection.
Digit display setting: 10 digits. Digit count can be changed. Real number calculation mode.
We perform an orthogonal projection of vector a—whose initial point is fixed at the origin—onto a line passing through the origin.
The initial point of the projected vector b is also the origin, and its terminal point lies at the point where a perpendicular line is dropped from the terminal point of a to the line.
Its length is equal to the norm of a multiplied by cosθ (where the angle is positive when measured counterclockwise).
The angle θ is determined by the value of the inverse tangent function with respect to the slope m of the line.
Therefore, we assume 0 < |m| < ∞ (-π/4 < θ < π/4).
Thus, θ is not the azimuth of the line’s direction unit vector itself. It is a numerical value used to determine the matrix element Ts
of the orthogonal projection.
Digit display setting: 10 digits. Digit count can be changed. Real number calculation mode.
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