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Update README.md
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asebian authored Jun 18, 2024
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Expand Up @@ -31,6 +31,7 @@ Please, **rather bookmark this site than the desmos URLs** since the latter will
* [Polarized wave](#polarized-wave)
5. [C1](#c1)
* [Complex number arithmetic](#complex-number-arithmetic)
* [Complex trigonometric functions][#complex-trigonometric-functions]


## R1
Expand All @@ -42,7 +43,7 @@ sin, arcsin, cos, arccos, tan, arctan, cot, arccot, sec, arcsec, csc, arccsc

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

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

Angle sum identities:

Expand All @@ -62,7 +63,7 @@ Natural logarithm, Euler number, exponential function and LambertW-function of r

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

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

## R2

Expand All @@ -71,92 +72,92 @@ Adding and subtracting vectors.

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

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

### Scalar multiplication
Scaling vectors.

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

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

### Inner product
Dot product

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

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

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

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

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

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

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

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

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

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

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

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

## R3

Expand All @@ -165,7 +166,7 @@ Sinoidal wave in temporal, spatial and spatiotemporal representation

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

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

## R4

Expand All @@ -174,29 +175,29 @@ Sinoidal oscillating membrane in canonical cross section views

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

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

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

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

## C1

### Complex number arithmetic

[https://www.desmos.com/calculator/kizjdicrvg](https://www.desmos.com/calculator/kizjdicrvg)

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

### Complex trigonometric functions

Expand All @@ -205,3 +206,6 @@ Sine, cosine, tangent, cotangent, secant, cosecant.
Application to parametric line (grid), circle, and square.

[https://www.desmos.com/calculator/kgsjcy7auy](https://www.desmos.com/calculator/kgsjcy7auy)


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

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