HowTo:Use Splines and Bezier Curves - Revision history

Bathurstfreak: /* About Bicubic Patches */

2007-12-09T10:04:26Z

About Bicubic Patches

2007-12-09T10:03:16Z

About Bicubic Patches

2007-12-09T09:20:35Z

Bezier Curves

2007-12-09T08:55:39Z

Splines

2007-12-09T08:52:11Z

Splines

2007-12-09T07:42:18Z

Splines

2007-12-09T07:39:24Z

Introduction

2007-12-08T22:06:53Z

New page: == Introduction == == Splines == == Bezier Curves == == About Bicubic Patches ==

New page

== Introduction ==

== Splines ==

== Bezier Curves ==

== About Bicubic Patches ==

@@ Line 53: / Line 53: @@
 The bezier patch has only four fixed points that is controlled by 12 reference points.
+<source lang="pov">
 #bicubic_patch {
    type 1 flatness 1 u_steps 3  v_steps 3
@@ Line 61: / Line 61: @@
    <0, 3, 2> <1, 3, 0> <2, 3, 0> <3, 3, -2>
+}

← Older revision		Revision as of 10:03, 9 December 2007
Line 48:		Line 48:

	== About Bicubic Patches ==		== About Bicubic Patches ==
		+
		+	If a Bezier curve is a 1 dimensional line on three dimensional space, then a bicubic patch is a 2 dimensional sheet on a three dimensional plane.
		+
		+	The bezier patch has only four fixed points that is controlled by 12 reference points.
		+
		+
		+	#bicubic_patch {
		+	type 1 flatness 1 u_steps 3 v_steps 3
		+	<0, 0, 2> <1, 0, 0> <2, 0, 0> <3, 0, -2>
		+	<0, 1, 0> <1, 1, 0> <2, 1, 0> <3, 1, 0>
		+	<0, 2, 0> <1, 2, 0> <2, 2, 0> <3, 2, 0>
		+	<0, 3, 2> <1, 3, 0> <2, 3, 0> <3, 3, -2>
		+	}

← Older revision		Revision as of 09:20, 9 December 2007
Line 37:		Line 37:

	== Bezier Curves ==		== Bezier Curves ==
		+
		+	Bezier Curves differ from other types of spline in that they only pass through the first and last control point and are simply influenced by the other intermediate control points.
		+	The equation for a bezier curve as used by POVRay is cubic and is of the form.
		+
		+	<math>B\left( t\right) = A \left( 1 - t\right)^3 + 3 B t \left( 1 - t\right)^2 + 3 C t^2\left( 1-t\right) + D t^3</math>
		+
		+	where t is from 0 to 1 and A, B, C and D represent a variable that may be a scalar or vector.
		+
		+	Consecutive bezier curves may be placed one after the other however the direction of the tangents at the start and end control point of joining curves must be identical.

	== About Bicubic Patches ==		== About Bicubic Patches ==

@@ Line 26: / Line 26: @@
    #declare count = count + 0.01;
 #end
 </source>

@@ Line 7: / Line 7: @@
 Splines may be of Linear, Quadratic or Cubic type of Spline and are accessed with the command #spline as shown below.
-#spline
+<source lang="pov">
-All splines pass through the intermediate
+#declare count = 0;
 == Bezier Curves ==
 == About Bicubic Patches ==

← Older revision		Revision as of 07:39, 9 December 2007
Line 1:		Line 1:
	== Introduction ==		== Introduction ==
		+
		+	All Curves and Patches utilised by POVRay are influenced by a number of control points. All curves pass through the start and the end control point, while most of the curves pass through the intermediate control points.

	== Splines ==		== Splines ==