Golden rectangle, a rectangle whose side lengths are in the golden ratio, 1 : 1 + 5 2 {\displaystyle 1:{\tfrac {1+{\sqrt {5 }}} {2 }}} 1:{\tfrac {1+{\sqrt {5 }}} {2}}, which is 1 : φ {\displaystyle 1:\varphi } 1:\varphi (the Greek letter phi), where φ {\displaystyle \varphi } \varphi is approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square. {1+{\sqrt {5 }}} approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square. {2 }}} {1+{\sqrt {5 }}} {2}}, which is 1 : φ {\displaystyle 1:\varphi } 1:\varphi (the Greek letter phi), where φ {\displaystyle \varphi } \varphi is approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square. {1+{\sqrt {5 }}} approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square. Golden rectangle, a rectangle whose side lengths are in the golden ratio, 1 : 1 + 5 2 {\displaystyle 1:{\tfrac {1+{\sqrt {5 }}} {1+{\sqrt {5 }}} {2}}, which is 1 : φ {\displaystyle 1:\varphi } 1:\varphi (the Greek letter phi), where φ {\displaystyle \varphi } \varphi is approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square. {1+{\sqrt {5 }}} approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square.
- Companion
- object
Value members
Inherited methods
The centre of the bounding rectangle. consider also using cenDefault.
The centre of the bounding rectangle. consider also using cenDefault.
- Inherited from
- BoundedElem
Currently throws, not sure if that is the correct behaviour. Creates a bounding rectangle for a collection of 2d points
Currently throws, not sure if that is the correct behaviour. Creates a bounding rectangle for a collection of 2d points
- Definition Classes
- Inherited from
- Polygon
The width of the BoundingRect of this object.
The width of the BoundingRect of this object.
- Inherited from
- BoundedElem
The centre of this geometric / graphical element. The centre will not change if the object type is capable of being rotated and is rotated. The cenDefault on other bounded elements may move relative to points on the object when the object is rotated.
The centre of this geometric / graphical element. The centre will not change if the object type is capable of being rotated and is rotated. The cenDefault on other bounded elements may move relative to points on the object when the object is rotated.
- Inherited from
- WithCentre
The default centre of this object is the centre. The centre will not change if the object type is capable of being rotated and is rotated.
The default centre of this object is the centre. The centre will not change if the object type is capable of being rotated and is rotated.
- Definition Classes
- Inherited from
- CentredElem
The centre point of this Polygon. The default centre for Polygons is the centre of the bounding rectangle.
The centre point of this Polygon. The default centre for Polygons is the centre of the bounding rectangle.
- Inherited from
- Polygon
Creates a PolygonCompound graphic that is active with a simple 1 colour fill and has a draw graphic for the Polygon. The default values for the draw area line width of 2 and a colour of Black.
Creates a PolygonCompound graphic that is active with a simple 1 colour fill and has a draw graphic for the Polygon. The default values for the draw area line width of 2 and a colour of Black.
- Inherited from
- Polygon
- Inherited from
- Polygon
- Inherited from
- Polygon
- Inherited from
- Polygon
- Inherited from
- Polygon
- Inherited from
- Polygon
Insert vertices before the specified insertion vertex.
Insert vertices before the specified insertion vertex.
- Inherited from
- Polygon
Map this collection of data elements to PolygonLike class of type BB.
Map this collection of data elements to PolygonLike class of type BB.
- Inherited from
- PolygonLike
- Inherited from
- Polygon
Determines if the parameter point lies inside this Polygon.
Determines if the parameter point lies inside this Polygon.
- Inherited from
- Polygon
Polygon side 1 from the last vertex to Vertex 1.
Polygon side 1 from the last vertex to Vertex 1.
- Inherited from
- Polygon3Plus
The centre or half way point of side 1 of this polygon. Side 1 starts at the vLast vertex and ends at the v1 vertex. This can be thought of as vertex 0.5.
The centre or half way point of side 1 of this polygon. Side 1 starts at the vLast vertex and ends at the v1 vertex. This can be thought of as vertex 0.5.
- Inherited from
- Polygon3Plus
The X component of the centre or half way point of side 1 of this polygon. Side 1 starts at the vLast vertex and ends at the v1 vertex. This can be thought of as vertex 0.5.
The X component of the centre or half way point of side 1 of this polygon. Side 1 starts at the vLast vertex and ends at the v1 vertex. This can be thought of as vertex 0.5.
- Inherited from
- Polygon3Plus
The Y component of the centre or half way point of side 1 of this polygon. Side 1 starts at the vLast vertex and ends at the v1 vertex. This can be thought of as vertex 0.5.
The Y component of the centre or half way point of side 1 of this polygon. Side 1 starts at the vLast vertex and ends at the v1 vertex. This can be thought of as vertex 0.5.
- Inherited from
- Polygon3Plus
Polygon side 2 from vertex 1 to vertex 2.
Polygon side 2 from vertex 1 to vertex 2.
- Inherited from
- Polygon3Plus
The centre or half way point of side 2 of this polygon. Side 2 starts at the v1 vertex and ends at the v2 vertex. This can be thought of as vertex 1.5
The centre or half way point of side 2 of this polygon. Side 2 starts at the v1 vertex and ends at the v2 vertex. This can be thought of as vertex 1.5
- Inherited from
- Polygon3Plus
The X component of the centre or half way point of side 2 of this polygon. Side 2 starts at the v1 vertex and ends at the v1 vertex. This can be thought of as vertex 1.5.
The X component of the centre or half way point of side 2 of this polygon. Side 2 starts at the v1 vertex and ends at the v1 vertex. This can be thought of as vertex 1.5.
- Inherited from
- Polygon3Plus
The Y component of the centre or half way point of side 3 of this polygon. Side 2 starts at the v1 vertex and ends at the v2 vertex. This can be thought of as vertex 1.5.
The Y component of the centre or half way point of side 3 of this polygon. Side 2 starts at the v1 vertex and ends at the v2 vertex. This can be thought of as vertex 1.5.
- Inherited from
- Polygon3Plus
The centre or half way point of side 3 of this polygon. Side 3 starts at the v2 vertex and ends at the v3 vertex. This can be thought of as vertex 2.5.
The centre or half way point of side 3 of this polygon. Side 3 starts at the v2 vertex and ends at the v3 vertex. This can be thought of as vertex 2.5.
- Inherited from
- Polygon3Plus
The X component of the centre or half way point of side 3 of this polygon. Side 3 starts at the v2 vertex and ends at the v3 vertex. This can be thought of as vertex 2.5.
The X component of the centre or half way point of side 3 of this polygon. Side 3 starts at the v2 vertex and ends at the v3 vertex. This can be thought of as vertex 2.5.
- Inherited from
- Polygon3Plus
The Y component of the centre or half way point of side 3 of this polygon. Side 3 starts at the v2 vertex and ends at the v3 vertex. This can be thought of as vertex 2.5.
The Y component of the centre or half way point of side 3 of this polygon. Side 3 starts at the v2 vertex and ends at the v3 vertex. This can be thought of as vertex 2.5.
- Inherited from
- Polygon3Plus
The centre or half way point of side 4 of this polygon. Side 4 starts at the v3 vertex and ends at the v4 vertex. This can be thought of as vertex 3.5.
The centre or half way point of side 4 of this polygon. Side 4 starts at the v3 vertex and ends at the v4 vertex. This can be thought of as vertex 3.5.
- Inherited from
- Polygon4Plus
The X component of the centre or half way point of side 4 of this polygon. Side 4 starts at the v3 vertex and ends at the v4 vertex. This can be thought of as vertex 3.5.
The X component of the centre or half way point of side 4 of this polygon. Side 4 starts at the v3 vertex and ends at the v4 vertex. This can be thought of as vertex 3.5.
- Inherited from
- Polygon4Plus
The Y component of the centre or half way point of side 4 of this polygon. Side 4 starts at the v3 vertex and ends at the v4 vertex. This can be thought of as vertex 3.5.
The Y component of the centre or half way point of side 4 of this polygon. Side 4 starts at the v3 vertex and ends at the v4 vertex. This can be thought of as vertex 3.5.
- Inherited from
- Polygon4Plus
Shear 2D geometric transformation along the X Axis on a Polygon, returns a Polygon. The return type will be narrowed in some but not all sub classes and traits.
Shear 2D geometric transformation along the Y Axis on a Polygon, returns a Polygon. The return type will be narrowed in sub classes and traits.
The 1st vertex, will throw on a 0 vertices polygon.
The 1st vertex, will throw on a 0 vertices polygon.
- Inherited from
- Polygon
The X component of the 1st vertex, will throw on a 0 vertices polygon.
The X component of the 1st vertex, will throw on a 0 vertices polygon.
- Inherited from
- Polygon
The Y component of the 1st vertex, will throw on a 0 vertices polygon.
The Y component of the 1st vertex, will throw on a 0 vertices polygon.
- Inherited from
- Polygon
The 2nd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The 2nd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon3Plus
The X component of the 2nd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The X component of the 2nd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon3Plus
The Y component of the 2nd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The Y component of the 2nd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon3Plus
The 3rd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The 3rd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon3Plus
The X component of the 3rd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The X component of the 3rd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon3Plus
The Y component of the 3rd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The Y component of the 3rd Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon3Plus
The 4th Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The 4th Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon4Plus
The X component of the 4th Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The X component of the 4th Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon4Plus
The Y component of the 4th Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
The Y component of the 4th Vertex. The default convention is for the vertices to be numbered in a clockwise direction with the 1st vertex immediately clockwise from 12 o'clock.
- Inherited from
- Polygon4Plus
This method should be overridden in final classes.
This method should be overridden in final classes.
- Inherited from
- PolygonLike
flatMap with index to an immutable Arr.
flatMap with index to an immutable Arr.
- Inherited from
- Polygon
Checks this polygon has at least 3 vertices.
Checks this polygon has at least 3 vertices.
- Inherited from
- PolygonLike
This method does nothing if the vertNum < 2. Foreach vertex applies the side effecting function to the previous vertex with each vertex. The previous vertex to the first vertex is the last vertex of the PolygonLike. Note the function signature (previous, vertex) => U follows the foreach based convention of putting the collection element 2nd or last as seen for example in fold methods'(accumulator, element) => B signature.
This method does nothing if the vertNum < 2. Foreach vertex applies the side effecting function to the previous vertex with each vertex. The previous vertex to the first vertex is the last vertex of the PolygonLike. Note the function signature (previous, vertex) => U follows the foreach based convention of putting the collection element 2nd or last as seen for example in fold methods'(accumulator, element) => B signature.
- Definition Classes
- Inherited from
- Polygon
A function that takes a 2D geometric transformation on a Pt2 as a parameter and performs the transformation on all the vertices returning a new transformed Polygon