OpenGL Study Notes (4): curve and Surface

Document directory

• 3.1 One-dimensional valuer
• 3.2 One-dimensional uniform Calculator
• 3.3 two-dimensional Calculator
• 4.1 select rendering Properties
• 4.2 create and draw a curve and Surface

By yurunsun@gmail.com
Sina Weibo @ sun yurun Sina Blog
Csdn blog

Date: 2013-6-13

Content of this chapter:

1. Concave Polygon partitioning
2. Quadratic equation Surface
3. Calculator
4. OpenGL

1. Concave Polygon partitioning

When OpenGL is used to display a concave polygon, it must be first decomposed into a simple convex polygon. This division method is called polygon partitioning (tesselation, returns a combination of triangles, triangle networks, triangle fans, and straight lines.

1. Create a new lattice object

   GLUtesselator* gluNewTess(void);

2. Register callback Functions

   void gluTessCallback(GLUtesselator *tessobj, GLenum type, void (*fn)());

3. Specify the lattice attribute, such as surround rules to determine which areas are filled and which areas are not colored.

   void gluTessProperty(GLUtesselator *tessobj, GLenum property, GLdouble value);void gluTessNormal(GLUtesselator *tessobj, GLdouble x, GLdouble y, GLdouble z);

4. Specify the contour lines of one or more closed polygon to render the divided polygon. It is best to put the divided Polygon into the display list.

   void gluTessBeginPolygon(GLUtesselator *tessobj, void *user_data);void gluNextContour(GLUtriangulatorObj *tessobj, GLenum type);void gluTessEndPolygon(GLUtesselator *tessobj);void gluTessBeginContour(GLUtesselator *tessobj);void gluNextContour(GLUtriangulatorObj *tessobj, GLenum type);void gluTessEndContour(GLUtesselator *tessobj);void gluTessVertex(GLUtesselator *tessobj, GLdouble coords[3], void *vertex_data);

5. Continue to use this lattice object or delete it

   void gluDeleteTess(GLUtesselator *tessobj);

2. quadratic equation Surface

Follow these steps to create and render the surface of a quadratic equation using Glu:

1. gluNewQuadric()Function creates a quadratic equation object
2. Specify the properties of the quadratic equation object
   • gluQuadricOrientation()The function controls the surround direction and distinguishes internal and external regions.
   • gluQuadricDrawStyle()Function Selection renders objects into points, straight lines, and filled Polygon
   • gluQuadricNormal()The function specifies a normal for each vertex or plane.
   • gluQuadricTexture()Texture coordinates generated by the function
3. gluQuadricCallback()Register an error handler for a function.

4. Call the surface rendering function of the corresponding quadratic equation as needed:

   gluSphere();gluCylinder();gluDisk();gluPartialDisk();

5. gluDeleteQuadric()Destroy quadratic equation objects

3. estimator 3.1 One-dimensional Calculator

GLfloat ctrlpoints[4][3] = {{ -4.0, -4.0, 0.0}, { -2.0, 4.0, 0.0},                             {2.0, -4.0, 0.0}, {4.0, 4.0, 0.0}};void init(void) {    glMap1f(GL_MAP1_VERTEX_3, 0.0, 1.0, 3, 4, &ctrlpoints[0][0]);    glEnable(GL_MAP1_VERTEX_3);}void display(void) {    glBegin(GL_LINE_STRIP);        for (int i = 0; i <= 30; i++)             glEvalCoord1f((GLfloat) i/30.0);    glEnd();}

Use the following function to define a one-dimensional calculator:

void glMap1f(GLenum target, float u1, float u2, GLint stride, GLint order, const float *points);GL_MAP1_VERTEX_3            //x, y, zvertex coordinatesGL_MAP1_VERTEX_4            //x, y, z, wvertex coordinatesGL_MAP1_INDEX               //color indexGL_MAP1_COLOR_4             //R, G, B, AGL_MAP1_NORMAL              //normal coordinatesGL_MAP1_TEXTURE_COORD_1     //stexture coordinatesGL_MAP1_TEXTURE_COORD_2     //s, ttexture coordinatesGL_MAP1_TEXTURE_COORD_3     //s, t, rtexture coordinatesGL_MAP1_TEXTURE_COORD_4     //s, t, r, qtexture coordinates

• Target: GlMap1Vertex_3 specifies the three-dimensional control points provided by the application and the three-dimensional vertices to be generated.
• U1: 0.0 indicates the low value of the parameter U
• U2: 1.0 indicates the high value of the U parameter.
• Stride: 3 indicates how many floating point values should be promoted from a control point to the next Control Point
• Order: 4 indicates the order of the spline.
• Points: & ctrlpoints [0] [0] indicates a pointer to the data at the first control point.

The following function is used to calculate an enabled calculator:

void glEvalCoord1{fd}(TYPE u);void glEvalCoord1{fd}v(const TYPE *u);

You can use multiple evaluators for computing at a time. That is, if you have defined and enabledGL_MAP1_VERTEX_3And oneGL_MAP1_COLOR_4You can call the 'glevalcoord1 () function to generate a position and a color at the same time.

3.2 One-dimensional uniform Calculator

In the above example, the courseware uses I/30, even if the U value is evenly distributed. The more convenient method is to callglMapGrid1f()The function defines a one-dimensional grid and then usesglEvalMesh1()Function Application Grid.

void glMapGrid1{fd}(GLint n, TYPE u1, TYPE u2);void glEvalMesh1(GLenum mode, GLint p1, GLint p2);

The second function is equivalent

glBegin(GL_POINTS);    for (i = p1; i <= p2; i++)         glEvalCoord1(u1 + i*(u2-u1)/n);glEnd();

3.3 two-dimensional Calculator

The difference from the one-dimensional calculator is that two Parameters u and v need to be considered.

void glMap2{fd}(GLenum target, TYPE u1, TYPE u2, GLint ustride,                GLint uorder,TYPE v1, TYPE v2, GLint vstride,                GLint vorder, TYPE points);void glEvalCoord2{fd}(TYPE u, TYPE v);void glEvalCoord2{fd}v(const TYPE *values);

There is also a two-dimensional even valuer:

void glMapGrid2{fd}(GLint nu,TYPE u1, TYPE u2, GLint nv,TYPE v1, TYPE v2);void glEvalMesh2(GLenummode, GLint i1, GLint i2, GLint j1, GLint j2);

4. API

Based on the functions of the OpenGL valuer, the Glu provides the interfaces for the use of NLE. The procedure is as follows:

1. glEnable(GL_AUTO_NORMAL)Automatically generate the normal (you can also calculate it yourself)
2. gluNewNurbsRENDERER()Create a pointer to a green chart object
3. gluNurbsProperty()Select rendering Properties
4. gluNurbsCallback()Error callback function Registration
5. gluBeginCurve()/gluBeginSurface()Declare to start plotting a curve and Surface
6. gluNurbsCurve()/gluNurbsSurface()Generate and render curve and Surface
7. gluEndCurve()/gluEndSurface()Declare end to draw a curve and Surface

The following describes several steps:

4.1 select rendering Properties

Struct (glunurbsobj * nobj, glenum property, glfloat value); glu_display_mode, // glu_fill, delimiter, delimiter, // delimiter, delimiter, // delimiter, // glu_path_lenth, glu_parametric_error, dependencies, glu_parametric_tolerance, glu_u_step, glu_v_step, glu_auto_load_matrix // do you need to download the projection matrix, modulo matrix, and viewport from the OpenGL server? Otherwise, use void gluloadsamplingmatrices, const glfloat modelmatrix [16], const glfloat projmatrix [16], const glint viewport [4]);

4.2 create and draw a curve and Surface

void gluNurbsSurface(GLUnurbsObj *nobj, GLint uknot_count,        GLfloat *uknot, GLint vknot_count, GLfloat *vknot,        GLint u_stride, GLint v_stride, GLfloat *ctlarray,        GLint uorder, GLint vorder, GLenum type);gluBeginSurface(nobj);    gluNurbsSurface(nobj, ..., GL_MAP2_TEXTURE_COORD_2);    gluNurbsSurface(nobj, ..., GL_MAP2_NORMAL);    gluNurbsSurface(nobj, ..., GL_MAP2_VERTEX_3);gluEndSurface(nobj);

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