Download Center Hexagon
Bethany Pensis
This however did not work how i wanted, this is because when the user clicks to the left of the centre point of a hexagon it snaps to the hexagon to the left of the one they clicked, and also if they click above the centre point on all odd columns it snaps to the hexagon above the one they clicked on.
The point clicked will always be closest to the center of hexagon in which the click occurs, unless the point is exactly between two hexagons in which case it will be equidistant from the two centers. The equation for the distance between two points is the SQRT( (x1-x2)^2 + (y1-y2)^2 ).
You do not have to test the distance to every hexagon. By creating x/y thresholds you can limit the test to just nearby hexagons. For example, if hexagons have a width of 10 and the point is at (51, 73) you do not have to test hexagons with x-coordinates of < 40 or > 70.
In fact this can be done quite easily mathematically, without resorting to the irritating, scale-limiting method of iterating through a large quantity of potential values. I came up with the following code in collusion with the excellent information at the following website. The secret is to imagine your hexagonal grid is actually a plane of three-dimensional cubes.
Actually, due to the regular shape of hexagons (all sides are the same length), this is as easy as cycling through your list of hexagonal tiles and figuring out which tile's center is closest to the mouse click.
I am a beginner to GH. I would like to draw trapezoid towards the center of the hexagonal grid. I fairly have an idea on what to do. I can probably draw lines towards the center point of the hexagon then draw circles in the center points of hexagon. then I can find the intersection of these two curves.
Thank you so much for the reply. But I have circles in the vertices of hexagonal grid. I need to have a trapezoid from the vertices of the intersection (circle and hex grid). Something like I have attached below. So when the radius of the circle increases the width of the trapezoid get narrow and vice versa.
Hi Aravind, here is a bit simpler approach based on the ExtendCurve and CurveClosestPoint components. No need to use the (relative) heavy intersection components: P.S.: I wasn't sure you need the circles on the hexagon corners for your design. If not you can just delete the group in grey.
For example, in the image below, I know the coordinates for GroupA (x=0, y=0, z=0) and GroupB (x=-1, y=1, z=0). How can I calculate the coordinates of the center tile of GroupB given that each group has the same radius (in this case the radius is 1) and they don't overlap each other (let's see it as a tiling of groups starting from 0,0,0 that creates a hex grid)?
In this simple example, I know as a human being that the center tile of GroupB is (x=-1, y=3, z=-2) but I need to code that logic in a way that a computer can calculate it for any given group on the map. I don't particularly need help on the code itself but the overall logic.
Based on the article I linked in my original question, I came up with an algorithm that calculates the small hexagon central coordinates based on its higher group coordinates (in this case, I've used a group with a radius of 10). I took the original algorithm and removed the area division the author did. The code is in javascript. The i, j and k variables are the cube coordinates of the group. The function returns the cube coordinates of the central small hex :
A hexagon is a six sided polygon. The sides of a hexagon are straight line segments. A hexagon is a planar figure, a figure that exists in a plane. A hexagon can be concave or convex. If a convex hexagon is equilateral (the sides are the same length), then the hexagon is a regular hexagon.
A regular hexagon is a six sided, equilateral, convex polygon. An equilateral polygon has sides that are all the same length. No line segment drawn between any two points in a convex figure leaves the figure.
- side or edge: One of the line segment that makes up hexagon. The length of a side of a regular hexagon will be denoted s in this article.
- vertex: Where two of the sides of the hexagon meet.
- interior: The area inside the hexagon.
- exterior: The area outside the hexagon.
- boundary: The sides and vertices of the hexagon.
- center: The point at the middle of the hexagon. The center of a regular hexagon can be found at the intersection of the perpendicular bisectors of any two sides. See How to Construct the Center, Incircle and Circumcircle of a Regular Hexagon. The center of a regular hexagon is also its centroid.
- incircle: A circle whose center is at the center of a regular hexagon that touches each side of the hexagon once. In this article, the radius of the incircle will be denoted r1.
- circumcircle: A circle whose center is at the center of a regular hexagon that intersects each of the vertices of the regular hexagon. In this article, the radius of the circumcircle will be denoted r2.
- apothem: A line segment from the center of a regular hexagon to the midpoint of one of the sides. The length of the apothem is the same as the radius of the incircle and is denoted (r1).
- sagitta: A line segment from the center of a side to the edge of the circumcircle of a regular hexagon that is collinear with the apothem.
- central angle:: The angle between two line segments extending from the center of the regular hexagon to two adjacent vertices. The central angle of a regular hexagon is always 72.
- interior angle: The angle between two adjacent sides. The interior angles of a regular hexagon always measure 120. The sum of the measures of interior angles of any convex hexagon is 720.
- exterior angle: The angle between the extended side of a regular hexagon and an adjacent side. The exterior angles of a regular hexagon always measure 60.
IllustrationFormulaDescription n = 6number of sides slength of a side p = 6sperimeter radius of the incircle r2 = sradius of the circumcircle area of the hexagon length of the apothem length of the sagitta α = 72measure of the central angles β = 120measure of the interior angles γ = 60measure of the exterior angles Table 1: Formulas for a regular hexagon.
StepIllustrationDescription and Justification 1 Draw a circle. Label the center of the circle a. This is given. 2 Draw a circle with the center on the circumference of circle a that is the same radius as circle a. Label the center of this circle b. 3 Label the intersections of the circles c and d. 4 Draw line segments ab, ac, ad, bc and bd. Note that all of these line segments are radii of congruent circles. This means that they are all the same length. So triangles Δabc and Δabd are equilateral triangles, triangles whose sides have the same measure. The angles of equilateral triangles also have the same measure. Therefore, triangles Δabc and Δabd are congruent by the SAS Congruence Theorem. 5 Draw another circle with the same radius as a with a center at c. Label the new intersection of circle c and circle a as e. 6 Draw another circle with the same radius as a with a center at e. Label the new intersection of circle e and circle a as f. Note that by the same arguments that were used in step 5, triangles Δabc and Δace are congruent equilateral triangles. 7 Continue the pattern until circles with centers at b, c, d, e, f and g are drawn. We know this is a regular hexagon because
- There are six sides. Count them.
- Each of the sides is a straight line segment. They were drawn as a straight line segment.
- The sides are all the same size. See the reasoning in step 4.
- The figure is a convex.
StepIllustrationDiscussion and Justification 1 The center of a regular hexagon is at the point of concurrency of perpendicular bisectors of any two sides that are not opposite each other. 2 Draw the perpendicular bisector of any side. 3 Draw the perpendicular bisector of any other side that is not opposite the side you used in step 2. 4 Label the intersection of the two perpendicular bisectors as 'center'. 5 Draw a circle with a center at the point labeled 'center' and the edge at a point where a perpendicular bisector intersects a side. Thisis the incircle. 6 Draw a circle with a center at the point labeled 'center' and the edge at any vertex. This is the circumcircle. Table 3 - How to construct the center, incircle and circumcircle of a regular hexagon
A tessellation of one or more polygon is an arrangement of those polygons that fills a plane. The are a number of tessellations that use hexagons. Most of the tessellations shown here use regular hexagons.
A regular tessellation of a hexagon. Three hexagons are around each vertex. A trihexagonal tiling. Each vertex has a regular hexagon, an equilateral triangle, a regular hexagon and an equilateral triangle. Table 4: tessellations of a hexagon
A hexagonal pavement. Hexagonal cloud formation on Saturn. A hexagonal mirror array. Carbon 36 fullerene molecules. Hexagonal basalt formation polished by a glacier. A hexagonal honeycomb. Table 5: Natural and Manufactured hexagons. Click on each image for more information on the image.
The content on the Website is made available for limited non-commercial, educational and personal use only, or for fair use as defined in the United States copyright laws. Users may download these files for their own use, subject to any additional terms or restrictions which may be applicable to the individual file or program. Users must, however, cite the author and source of the materials as they would material from any printed work, and the citations should include the URL \u201Cwww.clayartcenter.org,\u201D but not in any way that implies endorsement of the user or the user's use of the materials. By downloading, printing or otherwise using materials, whether accessed directly from the Website or via other sites or mechanisms, users agree that they will limit their use of such files to non-commercial, educational, personal or for fair use, and will not violate Clay Art Center\u2019s or any other party's proprietary rights. Users may not remove any copyright, trademark or other proprietary notices, including without limitation attribution information, credits and copyright notices that have been placed on or near the materials by Clay Art Center.
760c119bf3