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@asebian
asebian authored Jul 7, 2024
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Expand Up @@ -41,33 +41,33 @@ Real valued trigonometric functions, geometric reasoning with
help of the unit circle, identities, derivatives and antiderivatives:
sin, arcsin, cos, arccos, tan, arctan, cot, arccot, sec, arcsec, csc, arccsc

[https://www.desmos.com/calculator/5dms91pmgz](https://www.desmos.com/calculator/5dms91pmgz)
<https://www.desmos.com/calculator/5dms91pmgz>

![screenshot unit_trig-functions](img/trig_fnctns.png)

Angle sum identities:

[https://www.desmos.com/calculator/qs0vt2ojbh](https://www.desmos.com/calculator/qs0vt2ojbh)
<https://www.desmos.com/calculator/qs0vt2ojbh>

![screenshot angle sum identities](img/trigSum.png)

Angle difference identities:

[https://www.desmos.com/calculator/plyunzieof](https://www.desmos.com/calculator/plyunzieof)
<https://www.desmos.com/calculator/plyunzieof>

![screenshot angle difference identities](img/trigDiff.png)

### Hyperbolic functions
Hyperbolic sine, cosine, tangent and the unit hyperbola.

[https://www.desmos.com/calculator/bgqxibub4u](https://www.desmos.com/calculator/bgqxibub4u)
<https://www.desmos.com/calculator/bgqxibub4u>

![screenshot hyperbolic functions](img/hyptrig.png)

### ln, e, exp, W
Natural logarithm, Euler number, exponential function and LambertW-function of real values.

[https://www.desmos.com/calculator/fknzali1gx](https://www.desmos.com/calculator/fknzali1gx)
<https://www.desmos.com/calculator/fknzali1gx>

![screenshot nat. log, exp, W](img/ln_exp.png)

Expand All @@ -76,92 +76,92 @@ Natural logarithm, Euler number, exponential function and LambertW-function of r
### Vector addition
Adding and subtracting vectors.

[https://www.desmos.com/calculator/blx95ejvti](https://www.desmos.com/calculator/blx95ejvti)
<https://www.desmos.com/calculator/blx95ejvti>

![screenshot vector sum](img/vector_sum.png)

### Scalar multiplication
Scaling vectors.

[https://www.desmos.com/calculator/dnyvphayhr](https://www.desmos.com/calculator/dnyvphayhr)
<https://www.desmos.com/calculator/dnyvphayhr>

![screenshot scalar multiplication](img/scalar_mult.png)

### Inner product
Dot product

[https://www.desmos.com/calculator/7kxoinpssq](https://www.desmos.com/calculator/7kxoinpssq)
<https://www.desmos.com/calculator/7kxoinpssq>

![screenshot inner product](img/inner_product.png)

### Homogeneous coordinates
Transformation to and from homogeneous coordinates, normalization and far points.

[https://www.desmos.com/calculator/padkgx5uhb](https://www.desmos.com/calculator/padkgx5uhb)
<https://www.desmos.com/calculator/padkgx5uhb>

![screenshot homogeneous coordinates](img/homogen.png)

### Line equations
Line equation in standard form and derivation of parametric, slope-intercept, Hesse, polar and homogeneous coordinate forms.

[https://www.desmos.com/calculator/si4r5rrtkl](https://www.desmos.com/calculator/si4r5rrtkl)
<https://www.desmos.com/calculator/si4r5rrtkl>

![screenshot line equation standard form](img/line_standard_form.png)

### Rotation
Rotation of canonical base vectors, coordinates, and line equations.

[https://www.desmos.com/calculator/9mxcidhljn](https://www.desmos.com/calculator/9mxcidhljn)
<https://www.desmos.com/calculator/9mxcidhljn>

![screenshot rotation 2D](img/rotation_2D.png)

### Refraction
Refraction and inner reflection of a ray of light at a plane surface between two homogeneous media.

[https://www.desmos.com/calculator/gasu2wvno7](https://www.desmos.com/calculator/gasu2wvno7)
<https://www.desmos.com/calculator/gasu2wvno7>

![screenshot refraction](img/refraction.png)

### Curvature
Curvature and osculating circle of a continuously differentiable function.

[https://www.desmos.com/calculator/91xdbwxaxv](https://www.desmos.com/calculator/91xdbwxaxv)
<https://www.desmos.com/calculator/91xdbwxaxv>

![screenshot curvature](img/curvature.png)

### Bezier curve
De Castelau algorithm, Bernstein form, polynomial form, matrix form, derivatives and curvature of Bezier curves.

[https://www.desmos.com/calculator/5mxwdei16h](https://www.desmos.com/calculator/5mxwdei16h)
<https://www.desmos.com/calculator/5mxwdei16h>

![screenshot bezier curve](img/cubicbezier.png)

### Hermite curve
Polynomial and matrix form, derivatives, curvature, osculating circle, quarter circle approximation.

[https://www.desmos.com/calculator/ln1exvl9il](https://www.desmos.com/calculator/ln1exvl9il)
<https://www.desmos.com/calculator/ln1exvl9il>

![screenshot Hermite curve](img/hermite_spline.png)

### Cardinal curve
Polynomial and matrix form, derivatives, curvature, osculating circle, quarter circle approximation.

[https://www.desmos.com/calculator/06mclwqqur](https://www.desmos.com/calculator/06mclwqqur)
<https://www.desmos.com/calculator/06mclwqqur>

![screenshot cardinal curve](img/cardinal_curve.png)

### Catmull-Rom curve
Polynomial and matrix form, derivatives, curvature, osculating circle, quarter circle approximation.
(Cardinal curve with tension 0.5)

[https://www.desmos.com/calculator/z9slwnkvle](https://www.desmos.com/calculator/z9slwnkvle)
<https://www.desmos.com/calculator/z9slwnkvle>

![screenshot Catmull-Rom curve](img/catmull-rom.png)

### Rational Bezier curve
Circle, ellipse, parabola and hyperbola as rational Bezier curves in homogeneous coordinate matrix form.

[https://www.desmos.com/calculator/j3bnviwjqv](https://www.desmos.com/calculator/j3bnviwjqv)
<https://www.desmos.com/calculator/j3bnviwjqv>

![screenshot rational Bezier curve](img/rational_bezier.png)

Expand All @@ -170,7 +170,7 @@ Circle, ellipse, parabola and hyperbola as rational Bezier curves in homogeneous
### Sinoidal wave
Sinoidal wave in temporal, spatial and spatiotemporal representation

[https://www.desmos.com/calculator/lowmmrrnk2](https://www.desmos.com/calculator/lowmmrrnk2)
<https://www.desmos.com/calculator/lowmmrrnk2>

![screenshot sinoidal wave](img/sinoidalwave.png)

Expand All @@ -179,29 +179,29 @@ Sinoidal wave in temporal, spatial and spatiotemporal representation
### Circular wave
Sinoidal oscillating membrane in canonical cross section views

[https://www.desmos.com/calculator/piocwdyyo4](https://www.desmos.com/calculator/piocwdyyo4)
<https://www.desmos.com/calculator/piocwdyyo4>

![screenshot circular wave](img/circularwave.png)

### Flat wave
Sinoidal flat wave in canonical cross section views

[https://www.desmos.com/calculator/f1faftq0mt](https://www.desmos.com/calculator/f1faftq0mt)
<https://www.desmos.com/calculator/f1faftq0mt>

![screenshot flat wave](img/flatwave.png)

### Polarized wave
Elliptical, circular and linear polarization of a sinoidal wave in cross section view

[https://www.desmos.com/calculator/tcirqdnyt5](https://www.desmos.com/calculator/tcirqdnyt5)
<https://www.desmos.com/calculator/tcirqdnyt5>

![screenshot polarized wave](img/polwave.png)

## C1

### Complex number arithmetic

[https://www.desmos.com/calculator/7iak1wn5zg](https://www.desmos.com/calculator/7iak1wn5zg)
<https://www.desmos.com/calculator/7iak1wn5zg>

![screenshot complex numbers](img/complex.png)

Expand All @@ -211,6 +211,6 @@ Trigonometric functions of complex values in the complex number plane:
Sine, cosine, tangent, cotangent, secant, cosecant.
Application to parametric line (grid), circle, and square.

[https://www.desmos.com/calculator/nztgf6wjzu](https://www.desmos.com/calculator/nztgf6wjzu)
<https://www.desmos.com/calculator/nztgf6wjzu>

![screenshot complex trig-functions](img/complexTrig.png)

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