Tools

Ryan Hirst

Geogebra tools (.ggt) + worksheets showing their construction.

Table of Contents

  1. Lines, Rays, Segments
    1. Trimmed lines
    2. Tool: Trimmed Line, 3 points
    3. Segment Label
    4. Intersect Polygon and Ray
    5. Intersect Polygon and Line
    6. Intersect Polygon and Segment
    7. Intersect View Rectangle
    8. Tool: Light Reflection 1
  2. Triangles
    1. Tool: Altitude of a triangle
    2. Vectors: Incircle
  3. Arcs
    1. Arc Arrow 1
    2. Trimmed Arc 1
    3. Trace an Arc, 1
    4. Tool: Circular Arc
    5. Signed angle
  4. Interface (animation, etc)
    1. Make a Color Picker
    2. Natural Interpolation
    3. Simple Cubic Interpolation
    4. Interpolation 2: Rotation
  5. User Panel
    1. Screen Coordinates
    2. Parent, Child
    3. Floating Panel
    4. User Panel: Lines
    5. User Panel: Lines 2
    6. User panel: Circle
  6. More tools
    1. Ellipse from two vectors, 2
  7. Numerical Analysis
    1. Tool: Cubic Spline (Construction)

1.

Lines, Rays, Segments

  • 1. Trimmed lines
  • 2. Tool: Trimmed Line, 3 points
  • 3. Segment Label
  • 4. Intersect Polygon and Ray
  • 5. Intersect Polygon and Line
  • 6. Intersect Polygon and Segment
  • 7. Intersect View Rectangle
  • 8. Tool: Light Reflection 1

1.1.

Trimmed lines

Trimmed lines
– Ryan Hirst

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

Triangles

  • 1. Tool: Altitude of a triangle
  • 2. Vectors: Incircle

2.1.

Tool: Altitude of a triangle

Tool (.ggt): [url]http://www.geogebratube.org/material/show/id/87369[/url][br]Altitude[A,B,C, m]
Notes:[br]The angle that the altitude makes with the base is correct. This cannot be done with the tools in GGB, which uses a pretend angle system.
– Ryan Hirst

2.2.

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3.

Arcs

  • 1. Arc Arrow 1
  • 2. Trimmed Arc 1
  • 3. Trace an Arc, 1
  • 4. Tool: Circular Arc
  • 5. Signed angle

3.1.

Arc Arrow 1

The arc is [i]oriented.[/i] It respects the equivalence of these three statements:[br][math]\;\;\;[/math] Arc BC subtends central angle BAC,[br][math]\;\;\;[/math] There is a one-to-one correspondence between points on arc BC and points on segment BC.[br][math]\;\;\;[/math] The arc respects minimum rotation.[br][br]We may then preserve measure:[br]|BC| (magnitude) is the distance from B to C (direction).[br]|∡BAC| (magnitude) is the angle from B to C (direction/sign).
Arc Arrow 1
– Ryan Hirst

3.2.

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3.3.

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3.4.

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3.5.

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4.

Interface (animation, etc)

  • 1. Make a Color Picker
  • 2. Natural Interpolation
  • 3. Simple Cubic Interpolation
  • 4. Interpolation 2: Rotation

4.1.

Make a Color Picker

Make a Color Picker
– Ryan Hirst

4.2.

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4.3.

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4.4.

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5.

User Panel

  • 1. Screen Coordinates
  • 2. Parent, Child
  • 3. Floating Panel
  • 4. User Panel: Lines
  • 5. User Panel: Lines 2
  • 6. User panel: Circle

5.1.

Screen Coordinates

I would like points that stay put on the screen. Here are some requirements:[br]-stay pinned to screen coordinates[br]-stay in the viewport[br]-they may be freely moved[br]-we may use them as reference points for other objects.
Screen Coordinates
– Ryan Hirst

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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6.

More tools

  • 1. Ellipse from two vectors, 2

6.1.

Ellipse from two vectors, 2

The tool[br][math]\;\;[/math] MajorAxis[O, A, B, prv][br][math]\;\;\;\;[/math] prv, a free point[br][br]Gives points C, D.[br][br]Objects which transform the ellipse (here, points A, B, O) should update[br] SetValue[prv, C]
Ellipse from two vectors, 2
– Ryan Hirst

7.

Numerical Analysis

Tools to accompany the book [i]A First Course in Numerical Analysis[/i] by Anthony Ralston and Philip Rabinowitz.

  • 1. Tool: Cubic Spline (Construction)

7.1.

Tool: Cubic Spline (Construction)

Spline[<Points>, n, f'(a), f'(b)][br][br]gives the cubic spline passing through n equally spaced points, and with slopes f'(a), f'(b) at the endpoints.
Tool: Cubic Spline (Construction)
– Ryan Hirst

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