Calculate cubic bezier T value where tangent is perpendicular to anchor line.

Posted by drawnonward on Stack Overflow See other posts from Stack Overflow or by drawnonward
Published on 2010-04-20T05:22:34Z Indexed on 2010/04/20 5:43 UTC
Read the original article Hit count: 289

Filed under:

bezier

|

geometry

|

equation

Project a cubic bezier p1,p2,p3,p4 onto the line p1,p4. When p2 or p3 does not project onto the line segment between p1 and p4, the curve will bulge out from the anchor points. Is there a way to calculate the T value where the tangent of the curve is perpendicular to the anchor line?

This could also be stated as finding the T values where the projected curve is farthest from the center of the line segment p1,p4. When p2 and p3 project onto the line segment, then the solutions are 0 and 1 respectively. Is there an equation for solving the more interesting case?

The T value seems to depend only on the distance of the mapped control points from the anchor line segment.

I can determine the value by refining guesses, but I am hoping there is a better way.

© Stack Overflow or respective owner

Related posts about bezier

An extended Bezier Library or Algorithms of bezier operations

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi, Is there a library of data structures and operations for quadratic bezier curves? I need to implement: bezier to bitmap converting with arbitrary quality optimizing bezier curves common operations like subtraction, extraction, rendering etc. languages: c,c++,.net,python Algorithms without… >>> More
Quaddratic Bezier Curve: Calculate Tangent

as seen on Stack Overflow - Search for 'Stack Overflow'
Hello, I have have a quadratic bezier curve and I want to calculate the slope of the tangent in a given point. For example, let it be the middlepoint of the quadratic bezier curve, therefore t=0.5 (please see the link below for a picture of this). I've calculated the first derivation of the formula… >>> More
Quadratic Bezier Curve: Calculate Tangent

as seen on Stack Overflow - Search for 'Stack Overflow'
I have a quadratic bezier curve and I want to calculate the slope of the tangent in a given point. For example, let it be the middlepoint of the quadratic bezier curve, therefore t=0.5 (please see the link below for a picture of this). I've calculated the first derivative of the formula for the quadratic… >>> More
How do I draw part of parabola using iText ? Or how do I create quadratic bezier curves from cubic b

as seen on Stack Overflow - Search for 'Stack Overflow'
I need to draw a shape whose boundaries are parts of parabola (that is quadratic bezier curves) using iText. I have found only method for drawing cubic bezier curves in PdfContentByte class. So how do I draw quadratic bezier curves using iText ? One way would be to use method for cubic bezier curves… >>> More
GraphDisplay : a Bezier based control for graphing functions and curves

as seen on Code Project - Search for 'Code Project'
A WPF control for graphing functions, parametric curves, and polar curves >>> More

Related posts about geometry

GLSL check if fragment is on geometry

as seen on Stack Overflow - Search for 'Stack Overflow'
I am currently writing the positions of my geometry to the RGB channels of gl_FragColor and I would like to write 1.0 to the alpha channel if the fragment is part of geometry, and 0.0 if its empty. Is there a simple way to tell if a fragment is geometry or not? Maybe through gl_FragCoord.z? thanks >>> More
In JTS, when I do geometry.buffer(1).buffer(-1), will the resulting geometry be equivalent to the or

as seen on Stack Overflow - Search for 'Stack Overflow'
I was having problems while intersecting two geometries, getting a TopologyException probably due to a rounding error during the operation, then I read this fix and tried a buffer(0) on both input geometries, but still without success. Then I tried geo.buffer(1).buffer(-1) and it worked. Will these… >>> More
Multiple mesh with one geometry and diferent textures. Error

as seen on Stack Overflow - Search for 'Stack Overflow'
I have a loop where I create a multiple Mesh with different geometry, because each mesh has one texture: .... var geoCube = new THREE.CubeGeometry(voxelSize, voxelSize, voxelSize); var geometry = new THREE.Geometry(); for( var i = 0; i < voxels.length; i++ ){ var voxel = voxels[i]; var object; … >>> More
How to read verbose VC++ linker output

as seen on Stack Overflow - Search for 'Stack Overflow'
Trying to debug some linker errors, I turned on /VERBOSE and I'm trying to make sense of the output. It occurs to me that I really don't know how to read it. For example: 1>Compiling version info 1>Linking... 1>Starting pass 1 1>Processed /DEFAULTLIB:mfc80.lib 1>Processed /DEFAULTLIB:mfcs80… >>> More
Drawing a rectangular prism using opengl

as seen on Game Development - Search for 'Game Development'
I'm trying to learn opengl. I did some code for building a rectangular prism. I don't want to draw back faces so I used glCullFace(GL_BACK), glEnable(GL_CULL_FACE);. But I keep getting back faces also when viewing from front and also sometimes when rotating sides are vanishing. Can someone point me… >>> More