Teaching geometry to C++ Guy Davidson Meeting C++ 15/11/2019 - - PowerPoint PPT Presentation

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Teaching geometry to C++ Guy Davidson Meeting C++ 15/11/2019 - - PowerPoint PPT Presentation

Nov 13, 2022 96 likes •1.36k views

Teaching geometry to C++ Guy Davidson Meeting C++ 15/11/2019 @hatcat01 1 What to expect... 0. A brief history of geometry [4 - 22] 1. Linear algebra and geometry [24 - 57] 2. Lines and curves [59 - 82] 3. Polygons, regular and irregular [84

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Teaching geometry to C++

Guy Davidson Meeting C++ 15/11/2019 @hatcat01

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What to expect...

  • 0. A brief history of geometry [4 - 22]
  • 1. Linear algebra and geometry [24 - 57]
  • 2. Lines and curves [59 - 82]
  • 3. Polygons, regular and irregular [84 - 101]
  • 4. Intersection and precision [119 - 132]
  • 5. Summary of classes and functions [134 - 154]

@hatcat01

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What to expect...

  • 0. A brief history of geometry
  • 1. Linear algebra and geometry
  • 2. Lines and curves
  • 3. Polygons, regular and irregular
  • 4. Intersection and precision
  • 5. Summary of classes and functions

@hatcat01

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A Brief History Of Geometry

“The branch of mathematics concerned with questions of shape, size, relative position of figures and the properties

  • f space.”

@hatcat01

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A Brief History Of Geometry

“The branch of mathematics concerned with questions of shape, size, relative position of figures and the properties

  • f space.”

@hatcat01

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A Brief History Of Geometry

“The branch of mathematics concerned with questions of shape, size, relative position of figures and the properties

  • f space.”

@hatcat01

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A Brief History Of Geometry

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A Brief History Of Geometry

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A Brief History Of Geometry

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A Brief History Of Geometry

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René Descartes

  • b. 31st March 1596
  • d. 11th February 1650
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A Brief History Of Geometry

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Lots

  • Lots
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A Brief History Of Geometry

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x Lots

  • Lots
  • Lots

y Lots

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A Brief History Of Geometry

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A Brief History Of Geometry

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x,y in R {y - 2x - 3 = 0}

x y

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A Brief History Of Geometry

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y = 2x + 3

x y

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A Brief History Of Geometry

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x y

y = -x2

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A Brief History Of Geometry

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x y

x,y in R {x2 + y2 - 3 = 0}

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A Brief History Of Geometry

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x y

x,y in R, t in R, 0 <= t <= 2pi {x = 3 * sin(t), y = 3 * cos(t)}

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A Brief History Of Geometry

Other geometries

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A Brief History Of Geometry

Other geometries: Differential geometry

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A Brief History Of Geometry

Other geometries: Differential geometry Algebraic geometry

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A Brief History Of Geometry

Other geometries: Differential geometry Algebraic geometry Cartesian geometry

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What to expect...

  • 0. A brief history of geometry
  • 1. Linear algebra and geometry
  • 2. Lines and curves
  • 3. Polygons, regular and irregular
  • 4. Intersection and precision
  • 5. Summary of classes and functions

@hatcat01

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Linear Algebra And Geometry

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a1x1 + a2x2 + … + anxn = b

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Linear Algebra And Geometry

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a1x1 + a2x2 + … + anxn = b a1x1 + a2x2 = b

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Linear Algebra And Geometry

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a1x1 + a2x2 + … + anxn = b a1x1 + a2x2 = b ax + by = c

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Linear Algebra And Geometry

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a1x1 + a2x2 + … + anxn = b a1x1 + a2x2 = b ax + by = c by = -ax + c

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Linear Algebra And Geometry

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a1x1 + a2x2 + … + anxn = b a1x1 + a2x2 = b ax + by = c by = -ax + c y = mx + c

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Linear Algebra And Geometry

@hatcat01

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(x, y)

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Linear Algebra And Geometry

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(x, y) Translate (x, y) + (a, b) = (x+a, y+b)

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Scale (x, y) * 2 = (2x, 2y) (x, y) * (2 0) = (2x, 2y) (0 2)

Linear Algebra And Geometry

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Shear (x, y) * (1 2) = (x, 2x + y) (0 1)

Linear Algebra And Geometry

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Reflect (x, y) * (1 0) = (x, -y) (0 -1)

Linear Algebra And Geometry

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Rotate (x, y) * (cos a -sin a) (sin a cos a) = (x*cos a + y*sin a,

  • x*sin a + y*cos a)

Linear Algebra And Geometry

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Linear Algebra And Geometry

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Boost.Geometry

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Linear Algebra And Geometry

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Boost.Geometry Barend Gehrels

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Linear Algebra And Geometry

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Boost.Geometry Barend Gehrels Geometry classes

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Linear Algebra And Geometry

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Boost.Geometry Barend Gehrels Geometry classes Dimension agnostic

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Linear Algebra And Geometry

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Boost.Geometry Barend Gehrels Geometry classes Dimension agnostic Distance

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Linear Algebra And Geometry

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Boost.Geometry Barend Gehrels Geometry classes Dimension agnostic Distance Coordinate-system agnostic

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What to expect...

  • 0. A brief history of geometry
  • 1. Linear algebra and geometry
  • 2. Lines and curves
  • 3. Polygons, regular and irregular
  • 4. Intersection and precision
  • 5. Summary of classes and functions

@hatcat01

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Lines And Curves

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x,y in R {-3 <= x <= 5} {y = x/2 + 5/2}

x y

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Lines And Curves

struct line { float gradient; float y_intercept; };

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Lines And Curves

struct line { float gradient; float y_intercept; }; struct line_segment { point p1; point p2; };

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Lines And Curves

Q

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Lines And Curves

Q 3244.7482

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Lines And Curves

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Lines And Curves

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Lines And Curves

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Lines And Curves

class line { std::vector<point> points; };

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Lines And Curves

class line { float gradient; float intercept; };

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Lines And Curves

class line { float gradient; float intercept; point p1; point p2; };

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Lines And Curves

class line { float gradient; float intercept; point p_begin; point p_end; };

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Lines And Curves

Curves

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Lines And Curves

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y = x2

x y

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Lines And Curves

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Lines And Curves

class curve { point p1; point p2; point c1; point c2; };

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Lines And Curves

class curve { point p1; point p2; point c1; point c2; }; Quadratic Bézier curve

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Lines And Curves

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Lines And Curves

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Lines And Curves

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Lines And Curves

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Lines And Curves

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Lines And Curves

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Lines And Curves

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Lines And Curves

class curve { point p1; point p2; point control_point; };

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What to expect...

  • 0. A brief history of geometry
  • 1. Linear algebra and geometry
  • 2. Lines and curves
  • 3. Polygons, regular and irregular
  • 4. Intersection and precision
  • 5. Summary of classes and functions

@hatcat01

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

class triangle { point p1; point p2; point p3; };

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

class square { point p1; point p2; point p3; point p4; };

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Polygons, Regular And Irregular

class polygon { std::vector<point>; };

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Polygons, Regular And Irregular

class regular_polygon { point centre; point p; size_t vertex_count; float orientation; };

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Polygons, Regular And Irregular

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x Lots

  • Lots
  • Lots

y Lots

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

class circle { point centre; float radius; };

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

class ellipse { point focus_1; point focus_2; float radius; bool major; };

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

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class stadium { point focus_1; point focus_2; float radius; };

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Polygons, Regular And Irregular

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Polygons, Regular And Irregular

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class polycurve { std::vector<std::curve> segments; };

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Polygons, Regular And Irregular

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class polycurve { std::vector<std::pair<std::point>> segments; std::optional<point> end_point; };

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Polygons, Regular And Irregular

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What to expect...

@hatcat01

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  • 0. A brief history of geometry
  • 1. Linear algebra and geometry
  • 2. Lines and curves
  • 3. Polygons, regular and irregular
  • 4. Intersection and precision
  • 5. Summary of classes and functions
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Intersection And Precision

Intersection

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Intersection And Precision

Intersection y = x - 1 y = 2x - 4

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Intersection And Precision

Intersection y = x - 1 y = 2x - 4 0 = x - 3 x = 3

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Intersection And Precision

Intersection y = x2 y = x + 3.9

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Intersection And Precision

Intersection y = x2 y = x + 3.9 0 = x2 - x - 3.9 x = 0.5 ± √(4.15)

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Intersection And Precision

Intersection y = x - 2.3 y = x/3

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Intersection And Precision

Intersection y = x - 2.3 y = x/3 0 = 2x/3 - 2.3 x = 3.45

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Intersection And Precision

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Intersection And Precision

Round of applause for the brave volunteer

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Intersection And Precision

Round of applause for the brave volunteer Swords

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Intersection And Precision

Round of applause for the brave volunteer Swords Fast and thin

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Intersection And Precision

Round of applause for the brave volunteer Swords Fast and thin bool intersects(line a, line b);

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Intersection And Precision

Round of applause for the brave volunteer Swords Fast and thin bool intersects(line a, line b); FLT_MIN vs FLT_EPSILON

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Intersection And Precision

bool intersects(line a, line b, float epsilon);

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What to expect

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  • 0. A brief history of geometry
  • 1. Linear algebra and geometry
  • 2. Lines and curves
  • 3. Polygons, regular and irregular
  • 4. Intersection and precision
  • 5. Summary of classes and functions
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Summary Of Classes And Functions

std::math

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Summary Of Classes And Functions

std::math using float_2 = std::math::vector<fs_vector_engine<float, 2>>; using float_22 = std::math::matrix<fs_matrix_engine<float, 2, 2>>;

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Summary Of Classes And Functions

std::math using float_2 = std::math::vector<fs_vector_engine<float, 2>>; using float_22 = std::math::matrix<fs_matrix_engine<float, 2, 2>>; Implementer specialisation

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Summary Of Classes And Functions

std::math::path

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Summary Of Classes And Functions

std::math::path 3 (or 4?) control points

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Summary Of Classes And Functions

std::math::path 3 (or 4?) control points std::math::polyline

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Summary Of Classes And Functions

std::math::path 3 (or 4?) control points std::math::polyline std::math::polycurve

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Summary Of Classes And Functions

template <int N, typename coordinate_system> class regular_polygon;

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Summary Of Classes And Functions

template <int N, typename coordinate_system> class regular_polygon; template <typename coordinate_system> using triangle = regular_polygon<3, coordinate_system>;

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Summary Of Classes And Functions

template <int N, typename coordinate_system> class regular_polygon; template <typename coordinate_system> using triangle = regular_polygon<3, coordinate_system>; class circle;

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Summary Of Classes And Functions

template <int N, typename coordinate_system> class regular_polygon; template <typename coordinate_system> using triangle = regular_polygon<3, coordinate_system>; class circle; class ellipse;

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Summary Of Classes And Functions

template <int N, typename coordinate_system> class regular_polygon; template <typename coordinate_system> using triangle = regular_polygon<3, coordinate_system>; class circle; class ellipse; class stadium; (?)

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Summary Of Classes And Functions

template <int N, typename coordinate_system> class regular_polygon; template <typename coordinate_system> using triangle = regular_polygon<3, coordinate_system>; class circle; class ellipse; class stadium; (?) class patch;

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Summary Of Classes And Functions

intersect()

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Summary Of Classes And Functions

intersect() distance()

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Summary Of Classes And Functions

intersect() distance() length()

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Summary Of Classes And Functions

contains()

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Summary Of Classes And Functions

contains() area()

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Summary Of Classes And Functions

contains() area() perimeter()

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Summary Of Classes And Functions

contains() area() perimeter() centroid()

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Summary Of Classes And Functions

contains() area() perimeter() centroid() envelope()

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Thank You!

Ask me two questions.

@hatcat01

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Credits and acknowledgements

This was built using show.cpp which you can find at github.com/hatcat/show.cpp along with this presentation. show.cpp makes use of the C++ Standard Graphics proposal which you can find at github.com/cpp-io2d. Thanks to the io2d team for keeping things going. Thanks also to Hana Dusíková for prompting me to create a piece of open source C++ presentation software. Your move...

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