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// Copyright 2025-2026 肖其顿 (XIAO QI DUN)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package pdf
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import (
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"context"
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"fmt"
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"math"
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"slices"
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"sync"
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"github.com/xiaoqidun/pdfgo"
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)
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// meshVertex 保存局部毫米坐标及原曲面参数
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type meshVertex struct {
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point pdfgo.Point
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u, v float64
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}
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// MeshTriangle 保存按输出精度细分的曲面网格
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type MeshTriangle struct {
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vertices [3]meshVertex
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patch int
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}
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// meshSample 保存采样点参数，patch为一基编号，零表示未覆盖
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type meshSample struct {
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u, v float64
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patch int
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}
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// MeshRasterOptions 保存网格采样的坐标、精度及并行配置
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// Matrix将PDF页面坐标转换为毫米，Origin为输出块的毫米原点
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type MeshRasterOptions struct {
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Matrix pdfgo.Matrix
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Origin pdfgo.Point
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DPI float64
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Width, Height int
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Workers int
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SoftMask bool
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}
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// MeshEdge 按坐标及颜色分量匹配相邻三角形的共享边，不改变顶点顺序
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// 入参: previous 前一三角形, current 当前三角形
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// 返回: int OFD共享边标志，零表示独立三角形
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func MeshEdge(previous, current pdfgo.MeshTriangle) int {
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if previous.Points[2] != current.Points[1] || !slices.Equal(previous.Colors[2], current.Colors[1]) {
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return 0
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}
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for _, index := range [2]int{1, 0} {
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if previous.Points[index] == current.Points[0] && slices.Equal(previous.Colors[index], current.Colors[0]) {
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return 2 - index
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}
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}
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return 0
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}
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// MeshTriangles 按曲面二阶导数界细分，将几何误差控制在输出像素的十六分之一内
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// 入参: ctx 取消上下文, mesh 原始曲面, matrix 页面变换, dpi 输出精度
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// 返回: []MeshTriangle 细分结果, error 取消或坐标错误
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func MeshTriangles(ctx context.Context, mesh *pdfgo.MeshGradient, matrix pdfgo.Matrix, dpi float64) ([]MeshTriangle, error) {
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matrix = matrix.Mul(mesh.Matrix)
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var triangles []MeshTriangle
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for index, patch := range mesh.Patches {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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for i := range patch.Points {
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for j := range patch.Points[i] {
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patch.Points[i][j] = matrix.Apply(patch.Points[i][j])
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}
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}
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var duu, dvv, duv float64
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for i := 0; i < 4; i++ {
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for j := 0; j < 4; j++ {
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a := patch.Points[i][j]
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if i < 2 {
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b, c := patch.Points[i+1][j], patch.Points[i+2][j]
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duu = math.Max(duu, 6*math.Hypot(c.X-2*b.X+a.X, c.Y-2*b.Y+a.Y))
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}
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if j < 2 {
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b, c := patch.Points[i][j+1], patch.Points[i][j+2]
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dvv = math.Max(dvv, 6*math.Hypot(c.X-2*b.X+a.X, c.Y-2*b.Y+a.Y))
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}
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if i < 3 && j < 3 {
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b, c, d := patch.Points[i+1][j], patch.Points[i][j+1], patch.Points[i+1][j+1]
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duv = math.Max(duv, 9*math.Hypot(d.X-b.X-c.X+a.X, d.Y-b.Y-c.Y+a.Y))
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}
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}
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}
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steps := math.Max(1, math.Ceil(math.Sqrt(8*(duu+dvv+2*duv)*dpi/25.4)))
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if !finite(steps) || steps >= math.Sqrt(float64(int(^uint(0)>>1)/2)) {
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return nil, fmt.Errorf("mesh subdivision exceeds platform integer range")
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}
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n := int(steps)
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row := make([]meshVertex, n+1)
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for i := range row {
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if i%CompositeTileSize == 0 {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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}
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u := float64(i) / steps
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row[i] = meshVertex{patch.PointAt(u, 0), u, 0}
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}
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for j := 1; j <= n; j++ {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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v := float64(j) / steps
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left := meshVertex{patch.PointAt(0, v), 0, v}
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for i := 1; i <= n; i++ {
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u := float64(i) / steps
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right := meshVertex{patch.PointAt(u, v), u, v}
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a, b := row[i-1], row[i]
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triangles = append(triangles, MeshTriangle{[3]meshVertex{a, b, left}, index}, MeshTriangle{[3]meshVertex{b, right, left}, index})
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row[i-1], left = left, right
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}
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row[n] = left
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}
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}
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for index, triangle := range mesh.Triangles {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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vertices := [3]meshVertex{
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{matrix.Apply(triangle.Points[0]), 0, 0},
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{matrix.Apply(triangle.Points[1]), 1, 0},
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{matrix.Apply(triangle.Points[2]), 0, 1},
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}
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triangles = append(triangles, MeshTriangle{vertices, len(mesh.Patches) + index})
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}
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return triangles, nil
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}
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// MeshPixels 对输出块执行四倍超采样，曲面重叠按后补片及较大v、u取值
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// 入参: ctx 取消上下文, mesh 原曲面, triangles 已细分网格, space 混合空间, converter 已准备的颜色转换, options 采样配置
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// 返回: []ShadingPixel 颜色及覆盖, error 几何、颜色或取消错误
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func MeshPixels(ctx context.Context, mesh *pdfgo.MeshGradient, triangles []MeshTriangle, space *pdfgo.ColorSpace, converter pdfgo.ColorConverter, options MeshRasterOptions) ([]ShadingPixel, error) {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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const samples = 4
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w, h := options.Width*samples, options.Height*samples
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grid := make([]meshSample, w*h)
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scale := options.DPI / 25.4 * samples
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for _, triangle := range triangles {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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vertices := triangle.vertices
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for i := range vertices {
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vertices[i].point.X = (vertices[i].point.X - options.Origin.X) * scale
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vertices[i].point.Y = (vertices[i].point.Y - options.Origin.Y) * scale
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}
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a, b, d := vertices[0].point, vertices[1].point, vertices[2].point
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denominator := (b.Y-d.Y)*(a.X-d.X) + (d.X-b.X)*(a.Y-d.Y)
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if denominator == 0 {
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continue
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}
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minX, maxX := math.Min(a.X, math.Min(b.X, d.X)), math.Max(a.X, math.Max(b.X, d.X))
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minY, maxY := math.Min(a.Y, math.Min(b.Y, d.Y)), math.Max(a.Y, math.Max(b.Y, d.Y))
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if maxX < 0 || maxY < 0 || minX >= float64(w) || minY >= float64(h) {
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continue
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}
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endX := int(math.Min(float64(w), math.Ceil(maxX)))
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endY := int(math.Min(float64(h), math.Ceil(maxY)))
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for y := int(math.Max(0, math.Floor(minY))); y < endY; y++ {
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if err := ctx.Err(); err != nil {
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return nil, err
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}
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for x := int(math.Max(0, math.Floor(minX))); x < endX; x++ {
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px, py := float64(x)+.5, float64(y)+.5
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l0 := ((b.Y-d.Y)*(px-d.X) + (d.X-b.X)*(py-d.Y)) / denominator
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l1 := ((d.Y-a.Y)*(px-d.X) + (a.X-d.X)*(py-d.Y)) / denominator
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l2 := 1 - l0 - l1
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if l0 < -1e-10 || l1 < -1e-10 || l2 < -1e-10 {
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continue
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}
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u := math.Max(0, math.Min(1, l0*vertices[0].u+l1*vertices[1].u+l2*vertices[2].u))
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v := math.Max(0, math.Min(1, l0*vertices[0].v+l1*vertices[1].v+l2*vertices[2].v))
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current := &grid[y*w+x]
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if triangle.patch+1 > current.patch || triangle.patch+1 == current.patch && (v > current.v || v == current.v && u > current.u) {
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*current = meshSample{u, v, triangle.patch + 1}
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}
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}
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}
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}
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pixels := make([]ShadingPixel, options.Width*options.Height)
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var background [4]float64
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if mesh.Background != nil {
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var err error
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background, err = converter.Convert(mesh.Background[:mesh.Space.Components()])
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if err != nil {
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return nil, err
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}
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}
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var inverse pdfgo.Matrix
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if mesh.Bounds != nil {
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var ok bool
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inverse, ok = options.Matrix.Mul(mesh.Matrix).Inverse()
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if !ok {
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return nil, fmt.Errorf("singular mesh bounds transform")
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}
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}
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sampleRows := func(start, end int) error {
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colors := make(map[[4]float64][4]float64)
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colorants := PrepareShadingColorants(pdfgo.Paint{Mesh: mesh}, space, options.SoftMask)
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var sampler *pdfgo.MeshSampler
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if colorants == nil {
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sampler = mesh.NewSampler()
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}
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for y := start * samples; y < end*samples; y++ {
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if err := ctx.Err(); err != nil {
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return err
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}
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for x := 0; x < w; x++ {
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if box := mesh.Bounds; box != nil {
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point := inverse.Apply(pdfgo.Point{X: options.Origin.X + (float64(x)+.5)/scale, Y: options.Origin.Y + (float64(y)+.5)/scale})
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if point.X < box.XMin || point.X > box.XMax || point.Y < box.YMin || point.Y > box.YMax {
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continue
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}
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}
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sample := grid[y*w+x]
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if sample.patch == 0 && mesh.Background == nil {
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continue
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}
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values := background
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if sample.patch != 0 {
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var err error
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if colorants != nil {
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values, err = colorants.MeshAt(sample.patch-1, sample.u, sample.v)
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} else {
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values, err = sampler.ValuesAt(sample.patch-1, sample.u, sample.v)
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}
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if err != nil {
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return err
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}
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if cached, ok := colors[values]; ok {
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values = cached
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} else if colorants == nil {
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source := values
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values, err = converter.Convert(values[:mesh.Space.Components()])
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if err != nil {
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return err
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}
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if len(colors) == 2*CompositeTileSize {
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clear(colors)
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}
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colors[source] = values
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}
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}
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pixel := &pixels[(y/samples)*options.Width+x/samples]
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for i, value := range values {
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pixel.Values[i] += value
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}
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pixel.Shape++
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}
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}
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return ctx.Err()
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}
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workers := min(max(1, options.Workers), max(1, options.Height/32))
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if workers == 1 {
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if err := sampleRows(0, options.Height); err != nil {
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return nil, err
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}
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} else {
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var group sync.WaitGroup
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errors := make([]error, workers)
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for worker := range workers {
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group.Go(func() {
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errors[worker] = sampleRows(worker*options.Height/workers, (worker+1)*options.Height/workers)
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})
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}
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group.Wait()
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for _, err := range errors {
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if err != nil {
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return nil, err
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}
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}
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}
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for i := range pixels {
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pixel := &pixels[i]
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if pixel.Shape == 0 {
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continue
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}
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for j := range pixel.Values {
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pixel.Values[j] /= pixel.Shape
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}
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pixel.Shape /= samples * samples
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}
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return pixels, nil
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}
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