Transcript Framebuffer
The Rendering Pipeline CS 445/645 Introduction to Computer Graphics David Luebke, Spring 2003 Admin ● Call roll ● Assignment 0: questions? David Luebke 2 4/11/2016 Framebuffers ● So far we’ve talked about the physical display device ● How does the interface between the device and the computer’s notion of an image look? ● Framebuffer: A memory array in which the computer stores an image ■ On most computers, separate memory bank from main memory (why?) ■ Many different variations, motivated by cost of memory David Luebke 3 4/11/2016 Framebuffers: True-Color ● A true-color (aka 24-bit or 32-bit) framebuffer stores one byte each for red, green, and blue ● Each pixel can thus be one of 224 colors ● Pay attention to Endian-ness ● How can 24-bit and 32-bit mean the same thing here? David Luebke 4 4/11/2016 Framebuffers: Indexed-Color ● An indexed-color (8-bit or PseudoColor) framebuffer ● ● ● ● stores one byte per pixel (also: GIF image format) This byte indexes into a color map: How many colors can a pixel be? Still common on low-end displays (cell phones, PDAs, GameBoys) Cute trick: color-map animation David Luebke 5 4/11/2016 Framebuffers: Hi-Color ● Hi-Color is/was a popular PC SVGA standard ● Packs pixels into 16 bits: ■ 5 Red, 6 Green, 5 Blue (why would green get more?) ■ Sometimes just 5,5,5 ● Each pixel can be one of 216 colors ● Hi-color images can exhibit worse quantization artifacts than a well-mapped 8-bit image David Luebke 6 4/11/2016 Recap: Matrices ● By convention, matrix element Mrc is located at row r and column c: M11 M12 M21 M22 M Mm1 Mm2 M1n M2n Mmn ● By (OpenGL) convention, vectors are columns: David Luebke 7 v1 v v 2 v 3 4/11/2016 Recap: Matrices ● Matrix-vector multiplication applies a linear transformation to a vector: M11 M12 M13 vx M v M 21 M 22 M 23 vy M31 M32 M33 vz ● Recall how to do matrix multiplication David Luebke 8 4/11/2016 Recap: Matrix Transformations ● A sequence or composition of linear transformations corresponds to the product of the corresponding matrices ■ Note: the matrices to the right affect vector first, e.g: rotation about x, then translation along y, then rotation about z p ' R z Ty R x p ■ Note: order of matrices matters! PQx QPx ● The identity matrix I has no effect in multiplication Ix x ● Some (not all) matrices have an inverse: M 1 Mv v David Luebke 9 4/11/2016 Vectors and Matrices ● Vector algebra operations can be expressed in this matrix form ■ Dot product: ■ Cross product: ○ Note: use right-hand rule! a b ax ay bx az by bz 0 az ay bx cx a b az 0 ax by cy c ay ax 0 bz cz ac 0 bc 0 David Luebke 10 4/11/2016 The Rendering Pipeline: A Whirlwind Tour Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters David Luebke Rendering Pipeline 11 Framebuffer Display 4/11/2016 The Display You Know Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters David Luebke Rendering Pipeline 12 Framebuffer Display 4/11/2016 The Framebuffer You Know Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters David Luebke Rendering Pipeline 13 Framebuffer Display 4/11/2016 The Rendering Pipeline Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters David Luebke Rendering Pipeline 14 Framebuffer Display 4/11/2016 2-D Rendering: Rasterization (Coming Soon) Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters David Luebke Rendering Pipeline 15 Framebuffer Display 4/11/2016 The Rendering Pipeline: 3-D Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters David Luebke Rendering Pipeline 16 Framebuffer Display 4/11/2016 The Rendering Pipeline: 3-D Scene graph Object geometry Result: Modeling Transforms • All vertices of scene in shared 3-D “world” coordinate system Lighting Calculations • Vertices shaded according to lighting model Viewing Transform • Scene vertices in 3-D “view” or “camera” coordinate system Clipping Projection Transform David Luebke • Exactly those vertices & portions of polygons in view frustum • 2-D screen coordinates of clipped vertices 17 4/11/2016 The Rendering Pipeline: 3-D Scene graph Object geometry Result: Modeling Transforms • All vertices of scene in shared 3-D “world” coordinate system Lighting Calculations • Vertices shaded according to lighting model Viewing Transform • Scene vertices in 3-D “view” or “camera” coordinate system Clipping Projection Transform David Luebke • Exactly those vertices & portions of polygons in view frustum • 2-D screen coordinates of clipped vertices 18 4/11/2016 Rendering: Transformations ● So far, discussion has been in screen space ● But model is stored in model space (a.k.a. object space or world space) ● Three sets of geometric transformations: ■ Modeling transforms ■ Viewing transforms ■ Projection transforms David Luebke 19 4/11/2016 Rendering: Transformations ● Modeling transforms ■ Size, place, scale, and rotate objects parts of the model w.r.t. each other ■ Object coordinates world coordinates Y Y Z X X Z David Luebke 20 4/11/2016 Rendering: Transformations ● Viewing transform ■ Rotate & translate the world to lie directly in front of the camera ○ Typically place camera at origin ○ Typically looking down -Z axis ■ World coordinates view coordinates David Luebke 21 4/11/2016 Rendering: Transformations ● Projection transform ■ Apply perspective foreshortening ○ Distant = small: the pinhole camera model ■ View coordinates screen coordinates David Luebke 22 4/11/2016 Rendering: Transformations ● All these transformations involve shifting coordinate systems (i.e., basis sets) ● That’s what matrices do… ● Represent coordinates as vectors, transforms as matrices X cos q q Y sin sin q X q cos Y ● Multiply matrices = concatenate transforms! David Luebke 23 4/11/2016