Original Post
hi guys
i tried to reply this thread:
Extend curve to tube surface (part 1)
but seems not working anymore (?)
by the way, bit summary:
i have a curve (a bezier, but for tests and sketches i'm using a torus knot for semplicity) as a list of points, and i want to make a tubolar surface over it.
for that i have to find a frame, that is composed by 3 vectors: tangent, binormal and normal, in each point.
for that user jyk and apatriarca advice me to a parallel transform frame, good thecnique. it works!
it consists in calculate the first frame in first point and rotate it follow rotation angle of tangents.
i've found good reference:
Parallel Transport Approach to Curve Framing by Hanson and Ma
Game Programming Gems 2, The Parallel Transport Frame
in this previous post:
http://www.gamedev.net/community/forums/topic.asp?topic_id=577287
BUT:
#1 - find the first frame is a problem, i used approximations of frenet frame.
#2 - nowhere in reference i found that i need to recalculate cross product to find normal and binormals (!! how this is possible?? by the way thanks apatriarca you show me the way in last post)
#3 - in the end.. i found normal and binormal correctly but there was a big problem:
normals was switched: one directed inside, one outside.
i have to take the normal in previous frame but change it signs.
why???
here is my code, in pseudojava, hope this will be usefull for someone in future:
i hope this helps, strange that there is nowhere tutorials about this, it is a tech quite used for all tubolar-res
[Edited by - nkint on September 4, 2010 6:29:04 AM]
i tried to reply this thread:
Extend curve to tube surface (part 1)
but seems not working anymore (?)
by the way, bit summary:
i have a curve (a bezier, but for tests and sketches i'm using a torus knot for semplicity) as a list of points, and i want to make a tubolar surface over it.
for that i have to find a frame, that is composed by 3 vectors: tangent, binormal and normal, in each point.
for that user jyk and apatriarca advice me to a parallel transform frame, good thecnique. it works!
it consists in calculate the first frame in first point and rotate it follow rotation angle of tangents.
i've found good reference:
Parallel Transport Approach to Curve Framing by Hanson and Ma
Game Programming Gems 2, The Parallel Transport Frame
in this previous post:
http://www.gamedev.net/community/forums/topic.asp?topic_id=577287
BUT:
#1 - find the first frame is a problem, i used approximations of frenet frame.
#2 - nowhere in reference i found that i need to recalculate cross product to find normal and binormals (!! how this is possible?? by the way thanks apatriarca you show me the way in last post)
#3 - in the end.. i found normal and binormal correctly but there was a big problem:
normals was switched: one directed inside, one outside.
i have to take the normal in previous frame but change it signs.
why???
here is my code, in pseudojava, hope this will be usefull for someone in future:
Vec3D points[]; // curve point listVec3D tangents[];Vec3D binormals[];Vec3D normals[];void calculateFrames() { // first frame, needed by parallel transport frame approach // frenet method is used. // __approximations__ of tangents Vec3D p0, p1, b; p0 = points[0]; p1 = points[1]; tangents[0] = getTangentBetweenTwoPoint(p0, p1); p0 = points[1]; p1 = points[2]; tangents[1] = getTangentBetweenTwoPoint(p0, p1); b = tangents[0].cross(tangents[1]); b.normalize(); binormals[0] = b; normals[0] = b.cross(tangents[0]); // all tangents, needed for p.t.f. // again, __approximations__ // #1 for(int i=1; i<100-1; i++) { p0 = points; p1 = points[i+1]; tangents = getTangentBetweenTwoPoint(p0, p1); } // p.t.f approach: Vec3D old_normal; for(int i=1; i<100-2; i++) { p0 = tangents; p1 = tangents[i+1]; // this is what is called A in game programming gems // and B in Hanson and Ma article b = p0.cross(p1); b.normalize(); // normals theta = acos(p0.dot(p1)); old_normal = normals[i-1]; old_normal.normalize(); old_normal.rotateAroundAxis(b,theta); // here switching signs. no reference, no understanding, // empirical method founded for random choice. // #3 old_normal.x = -old_normal.x; old_normal.y = -old_normal.y; old_normal.z = -old_normal.z; // ma questi due ulteriori cross da dove vengono fuori?! // #2 binormals = tangents.cross(old_normal); normals = tangents.cross(binormals); println("it should be PI/2: "+PI/2); // println(Vec3D.angleBetween(binormals, tangents)); // println(Vec3D.angleBetween(normals, tangents)); // println(Vec3D.angleBetween(normals, binormals)); // assertation tests here }}i hope this helps, strange that there is nowhere tutorials about this, it is a tech quite used for all tubolar-res
[Edited by - nkint on September 4, 2010 6:29:04 AM]
