Automesher application extends autocad and bricscad software with functionality to import and. I need to triangulate a polygon for rendering in opengl es on android no glu triangulation available. I came up with an algorhythm on my own which i later found was the line sweep algorythm, but i am too lazy to implement it on my own. Convex and nonconvex polygons for more great videos, visit. In real life, a stop sign is an example of a convex polygon, and a cross is an example of a concave polygon. If the plane and the plane containing the polygon are not parallel, then there is possibly. The edges v 2 v 3 and v 4 v 5 intersect the plane, and the intersection consists of a single line shown in bold.
Triangulating simple convex polygons is peanuts, but triangulating nonconvex ones appears to be quite an involved process. Two methods for antialiased wireframe drawing with hidden line. Consider each edge e of clipping area and do following. One approach for drawing nonconvex polygons is to break them down into triangles. Implement the scanline filling algorithm for polygons including nonconvex and nonsimple polygons described in class.
Only after being subdivided into convex polygons, these non convex polygons can be accepted by the opengl rendering pipeline. However, we cannot use the same method to calculate the area, as one of. In the pictures above, for example, note that while the jaggies on the lines are reduced, the polygon edges in the lower left appear just the same. Instead, opengl is a polygonbased rendering system which. Scanline polygon filling using opengl in c geeksforgeeks. A concave polygon will always have at least one reflex interior anglethat is, an angle with a measure that is between 180 degrees and 360 degrees exclusive some lines containing interior points of a concave polygon intersect its boundary at more than two points. A convex polygon and a convex clipping area are given. Nonconvex and nonsimple polygons are expensive to process and render convexity and simplicity is expensive to test behavior of opengl implementation on disallowed polygons is undefined some tools in glu for decomposing complex polygons tessellation triangles are most efficient. Convex hull dnc 365 convexity you know what convex means, right. All points on line segment between two points in a polygon are also in the polygon flat. Measuring regularity of convex polygons sciencedirect. A nonconvex regular polygon is called a regular star polygon.
Be aware that if you present opengl with a nonconvex filled polygon, it might not draw it as you. In case youre wondering, im writing a programlibrarywhatever that will give you names. This answer shares content with my recent answer to a similar question here. The input will be a list or array of vertices in counterclockwise order. There are a number of algorithms that can do this, which can be found by searching for keywords like polygon triangulation. How to force opengl to draw a nonconvex filled polygon. To optimize performance, the basic opengl only renders convex polygons, but the glu contains routines to tessellate concave polygons into convex ones, which the basic opengl can handle.
What im doing, basically, is tessellate the polygon and create a display list from that. The basic procedure of tessellation is sending all vertex coordinates of a non convex polygon to the tessellator instead of sending them directly to opengl rendering pipeline, and then tessellating the polygon by the tessellator. Polygon rendering and opengl 3dimensional objects bounded by planar surfaces facets a planar facet is defined by an ordered set of 3d vertices, lying on one plane, which form a closed polygon, straight lines are drawn1. Im just answering this question because it showed up at the top of my feed, nothing fancy. A convex polygon is a simple polygon not selfintersecting in which no line segment between two points on the boundary ever goes outside the polygon. This includes concave polygons, selfintersecting polygons, and polygons with holes. Complex primitives will not be rendered correctly by the opengl api directly. This means that makers of opengl hardware and drivers have some leeway in deciding what exactly happens when you request antialiasing. Highlights measures to evaluate to which extent a convex polygon is close to be regular. Mean value coordinates for arbitrary planar polygons uio. The basic procedure of tessellation is sending all vertex coordinates of a nonconvex polygon to the. With the left mouse button click, draw polygons, then click the right mouse button and judgment polygon convex concave, if polygonal concave polygon, you are prompted for the concave polygon, if is a convex polygon suggests is a convex polygon. Opengl has another mechanism that works great for this.
The measures satisfy requirements that guarantee them to be well defined. Outline nonconvex polygon in opengl stack overflow. Input is in the form of vertices of the polygon in clockwise order. Simple polygon nonsimple polygons by jordan theorem, a polygon divides the plane into interior, exterior, and boundary. Nonconvex and nonsimple polygons are expensive to process and render convexity and simplicity is expensive to test better to fix polygons as a preprocessing step behavior of opengl implementation on.
Different geometric characteristics of regularity are used to define the measures. For nonconvex polygons a usual approach is to triangulate the domain and. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. How to force opengl to draw a nonconvex filled polygon stack. To fill those figures with color, we need to develop some algorithm. A simple polygon that is not convex is called concave, nonconvex or reentrant.
First, the edges of opengl polygons cant intersect a mathematician would call a polygon satisfying this condition a simple polygon. Second, opengl polygons must be convex, meaning that they cannot have indentations. They are nonconvex, and they cant be drawn with a boundary made up of a single closed loop. While clipping for non convex polygons without holes might not be that difficult, i think for polygons with holes you might need to do a convex decomposition and perform the clipping as normal. Opengl, however, doesnt restrict the number of line segments making up the boundary of a convex polygon. Opengl which define a simple linear interpolation mode. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Our algorithm requires two descriptions for each object. The index bisection method for convex polygons that supported an olog n query does not apply to convex. The behavior of antialiasing in opengl is implementationdependent. Time for action tessellating a polygon openscenegraph. Polygon issues opengl will only display triangles simple.
Experimental results are shown and discussed, for all the proposed. It works for nondegenerate convex or nonconvex polyhedra, which are given by their vertices and oriented facets. Minimum convex polygon software free download minimum. Im looking for an algorithm to partition any simple closed polygon into convex sub polygons preferably as few as possible. An accurate computation of the distance between a point. Draw a polygon take any two points inside the polygon, not on the edges join those two points with a straight line if that straight line completely. We propose a simple modification to the classical polygon rasterization pipeline that enables exact, efficient raycasting of bounded implicit surfaces without the use of a global spatial data structure or bounding hierarchy. Download polygon mesh freeware free polygon mesh downloads. A nonconvex regular polygon is a regular star polygon. Opengl can directly display only simple convex polygons. Algorithms to compute the measures are described, and their complexity is analyzed.
Midpoint polygon to a nonconvex quadrilateral as was the case for convex quadrilaterals, the midpoint polygon is a parallelogram with sides parallel to the diagonals of the original quadrilateral. For example, opengl automatically splits a pentagonal. Cecs 361 computer graphics i university of missouri. For example, to draw nonconvex polygons, one can subdivide them into. The most common example is the pentagram, which has the same vertices as a pentagon, but connects alternating vertices. Contribute to sprintropengl examples development by creating an account on github. Opengl supports a handful of primitive types for modeling twodimensional 2d.
In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. A polygon which has all its sides and angles equal is called a regular polygon. The method for solving this is a simple generalization of the technique for intersecting a triangle and a plane section 11. Create a sorted edge table, which is a table of edges sorted by their smallest ycoordinate. Line segments called edges, their endpoints called vertices.
One approach for drawing non convex polygons is to break them down into triangles. Ive been looking for an algorithm that clips polygon in 2d by a line. Opengl library organization glu opengl utility library. Only after being subdivided into convex polygons, these nonconvex polygons can be accepted by the opengl rendering pipeline. Is there an already known algorithm for polygon triangulation. Converts a raw digitized polygon mesh to a clean mesh where all the occurrences of a specific set of defects are corrected. Other generalizations of barycentric coordinates to convex polygons and even to the kernel of a star. If nothing happens, download github desktop and try again. The task is to clip polygon edges using the sutherlandhodgman algorithm. Equivalently, it is a simple polygon whose interior is a convex set. Tesselation of mono connected non convex polygon codeproject. Ive tried lots of times to get this to work but, no luck. Opengl polygons must be convex a simple, but not convex b nonsimple convex why polygon restrictions. A convex polygon is the opposite of a concave polygon.
Polygon mesh freeware for free downloads at winsite. As we saw in the previous chapter, a convex polygon can be represented by a triangle fan so opengl tries to draw the. Scanline polygon filling using opengl in c figures on a computer screen can be drawn using polygons. Stated precisely, a region is convex if, given any two points in the interior, the line segment joining them is also in the. Im trying to draw an outlined nonconvex polygon in opengl, but im being unsuccessful, hence the question.