Implement phong illumination
This commit is contained in:
parent
cf1a540808
commit
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24 changed files with 1795 additions and 0 deletions
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assignment-1b/.gitignore
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assignment-1b/.gitignore
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/target
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/assignment-1
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/examples/*.png
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*.ppm
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*.zip
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*.pdf
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0
assignment-1b/ASSIGNMENT.md
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0
assignment-1b/ASSIGNMENT.md
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649
assignment-1b/Cargo.lock
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assignment-1b/Cargo.lock
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# This file is automatically @generated by Cargo.
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# It is not intended for manual editing.
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version = 3
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"num-traits",
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"bitflags",
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"clap_derive",
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"clap_lex",
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"is-terminal",
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"once_cell",
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"strsim",
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"termcolor",
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]
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[[package]]
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dependencies = [
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"heck",
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"proc-macro-error",
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"proc-macro2",
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"quote",
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"syn",
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]
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[[package]]
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name = "clap_lex"
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dependencies = [
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"os_str_bytes",
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]
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[[package]]
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name = "crossbeam-channel"
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dependencies = [
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"cfg-if",
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"crossbeam-utils",
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]
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[[package]]
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name = "crossbeam-deque"
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dependencies = [
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"cfg-if",
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"crossbeam-epoch",
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"crossbeam-utils",
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]
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[[package]]
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name = "crossbeam-epoch"
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dependencies = [
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"autocfg",
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"cfg-if",
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"crossbeam-utils",
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"memoffset",
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"scopeguard",
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]
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[[package]]
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dependencies = [
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"cfg-if",
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]
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[[package]]
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dependencies = [
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"proc-macro2",
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"quote",
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"syn",
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]
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[[package]]
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[[package]]
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dependencies = [
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"errno-dragonfly",
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"libc",
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"winapi",
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]
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[[package]]
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"cc",
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"libc",
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]
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[[package]]
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"libc",
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]
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[[package]]
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]
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[[package]]
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"hermit-abi",
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"io-lifetimes",
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"rustix",
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"windows-sys",
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]
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[[package]]
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name = "libc"
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[[package]]
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[[package]]
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"num-traits",
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"typenum",
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[[package]]
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]
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[[package]]
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]
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[[package]]
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name = "num-traits"
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||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
dependencies = [
|
||||||
|
"autocfg",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "num_cpus"
|
||||||
|
version = "1.15.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "0fac9e2da13b5eb447a6ce3d392f23a29d8694bff781bf03a16cd9ac8697593b"
|
||||||
|
dependencies = [
|
||||||
|
"hermit-abi",
|
||||||
|
"libc",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "once_cell"
|
||||||
|
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|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
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|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "ordered-float"
|
||||||
|
version = "3.4.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
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|
||||||
|
dependencies = [
|
||||||
|
"num-traits",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "os_str_bytes"
|
||||||
|
version = "6.4.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "9b7820b9daea5457c9f21c69448905d723fbd21136ccf521748f23fd49e723ee"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "paste"
|
||||||
|
version = "1.0.11"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "d01a5bd0424d00070b0098dd17ebca6f961a959dead1dbcbbbc1d1cd8d3deeba"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "proc-macro-error"
|
||||||
|
version = "1.0.4"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "da25490ff9892aab3fcf7c36f08cfb902dd3e71ca0f9f9517bea02a73a5ce38c"
|
||||||
|
dependencies = [
|
||||||
|
"proc-macro-error-attr",
|
||||||
|
"proc-macro2",
|
||||||
|
"quote",
|
||||||
|
"syn",
|
||||||
|
"version_check",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "proc-macro-error-attr"
|
||||||
|
version = "1.0.4"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "a1be40180e52ecc98ad80b184934baf3d0d29f979574e439af5a55274b35f869"
|
||||||
|
dependencies = [
|
||||||
|
"proc-macro2",
|
||||||
|
"quote",
|
||||||
|
"version_check",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "proc-macro2"
|
||||||
|
version = "1.0.50"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "6ef7d57beacfaf2d8aee5937dab7b7f28de3cb8b1828479bb5de2a7106f2bae2"
|
||||||
|
dependencies = [
|
||||||
|
"unicode-ident",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "quote"
|
||||||
|
version = "1.0.23"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "8856d8364d252a14d474036ea1358d63c9e6965c8e5c1885c18f73d70bff9c7b"
|
||||||
|
dependencies = [
|
||||||
|
"proc-macro2",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "rawpointer"
|
||||||
|
version = "0.2.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "60a357793950651c4ed0f3f52338f53b2f809f32d83a07f72909fa13e4c6c1e3"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "rayon"
|
||||||
|
version = "1.6.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "6db3a213adf02b3bcfd2d3846bb41cb22857d131789e01df434fb7e7bc0759b7"
|
||||||
|
dependencies = [
|
||||||
|
"either",
|
||||||
|
"rayon-core",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "rayon-core"
|
||||||
|
version = "1.10.2"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "356a0625f1954f730c0201cdab48611198dc6ce21f4acff55089b5a78e6e835b"
|
||||||
|
dependencies = [
|
||||||
|
"crossbeam-channel",
|
||||||
|
"crossbeam-deque",
|
||||||
|
"crossbeam-utils",
|
||||||
|
"num_cpus",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "rustix"
|
||||||
|
version = "0.36.7"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "d4fdebc4b395b7fbb9ab11e462e20ed9051e7b16e42d24042c776eca0ac81b03"
|
||||||
|
dependencies = [
|
||||||
|
"bitflags",
|
||||||
|
"errno",
|
||||||
|
"io-lifetimes",
|
||||||
|
"libc",
|
||||||
|
"linux-raw-sys",
|
||||||
|
"windows-sys",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "safe_arch"
|
||||||
|
version = "0.6.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "794821e4ccb0d9f979512f9c1973480123f9bd62a90d74ab0f9426fcf8f4a529"
|
||||||
|
dependencies = [
|
||||||
|
"bytemuck",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "scopeguard"
|
||||||
|
version = "1.1.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "d29ab0c6d3fc0ee92fe66e2d99f700eab17a8d57d1c1d3b748380fb20baa78cd"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "serde"
|
||||||
|
version = "1.0.152"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "bb7d1f0d3021d347a83e556fc4683dea2ea09d87bccdf88ff5c12545d89d5efb"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "simba"
|
||||||
|
version = "0.8.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "50582927ed6f77e4ac020c057f37a268fc6aebc29225050365aacbb9deeeddc4"
|
||||||
|
dependencies = [
|
||||||
|
"approx",
|
||||||
|
"num-complex",
|
||||||
|
"num-traits",
|
||||||
|
"paste",
|
||||||
|
"wide",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "strsim"
|
||||||
|
version = "0.10.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "73473c0e59e6d5812c5dfe2a064a6444949f089e20eec9a2e5506596494e4623"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "syn"
|
||||||
|
version = "1.0.107"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "1f4064b5b16e03ae50984a5a8ed5d4f8803e6bc1fd170a3cda91a1be4b18e3f5"
|
||||||
|
dependencies = [
|
||||||
|
"proc-macro2",
|
||||||
|
"quote",
|
||||||
|
"unicode-ident",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "termcolor"
|
||||||
|
version = "1.2.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "be55cf8942feac5c765c2c993422806843c9a9a45d4d5c407ad6dd2ea95eb9b6"
|
||||||
|
dependencies = [
|
||||||
|
"winapi-util",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "typenum"
|
||||||
|
version = "1.16.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "497961ef93d974e23eb6f433eb5fe1b7930b659f06d12dec6fc44a8f554c0bba"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "unicode-ident"
|
||||||
|
version = "1.0.6"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "84a22b9f218b40614adcb3f4ff08b703773ad44fa9423e4e0d346d5db86e4ebc"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "version_check"
|
||||||
|
version = "0.9.4"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "49874b5167b65d7193b8aba1567f5c7d93d001cafc34600cee003eda787e483f"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "wide"
|
||||||
|
version = "0.7.5"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "ae41ecad2489a1655c8ef8489444b0b113c0a0c795944a3572a0931cf7d2525c"
|
||||||
|
dependencies = [
|
||||||
|
"bytemuck",
|
||||||
|
"safe_arch",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "winapi"
|
||||||
|
version = "0.3.9"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
|
||||||
|
dependencies = [
|
||||||
|
"winapi-i686-pc-windows-gnu",
|
||||||
|
"winapi-x86_64-pc-windows-gnu",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "winapi-i686-pc-windows-gnu"
|
||||||
|
version = "0.4.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "winapi-util"
|
||||||
|
version = "0.1.5"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "70ec6ce85bb158151cae5e5c87f95a8e97d2c0c4b001223f33a334e3ce5de178"
|
||||||
|
dependencies = [
|
||||||
|
"winapi",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "winapi-x86_64-pc-windows-gnu"
|
||||||
|
version = "0.4.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows-sys"
|
||||||
|
version = "0.42.0"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "5a3e1820f08b8513f676f7ab6c1f99ff312fb97b553d30ff4dd86f9f15728aa7"
|
||||||
|
dependencies = [
|
||||||
|
"windows_aarch64_gnullvm",
|
||||||
|
"windows_aarch64_msvc",
|
||||||
|
"windows_i686_gnu",
|
||||||
|
"windows_i686_msvc",
|
||||||
|
"windows_x86_64_gnu",
|
||||||
|
"windows_x86_64_gnullvm",
|
||||||
|
"windows_x86_64_msvc",
|
||||||
|
]
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_aarch64_gnullvm"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "8c9864e83243fdec7fc9c5444389dcbbfd258f745e7853198f365e3c4968a608"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_aarch64_msvc"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "4c8b1b673ffc16c47a9ff48570a9d85e25d265735c503681332589af6253c6c7"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_i686_gnu"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "de3887528ad530ba7bdbb1faa8275ec7a1155a45ffa57c37993960277145d640"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_i686_msvc"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "bf4d1122317eddd6ff351aa852118a2418ad4214e6613a50e0191f7004372605"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_x86_64_gnu"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "c1040f221285e17ebccbc2591ffdc2d44ee1f9186324dd3e84e99ac68d699c45"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_x86_64_gnullvm"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "628bfdf232daa22b0d64fdb62b09fcc36bb01f05a3939e20ab73aaf9470d0463"
|
||||||
|
|
||||||
|
[[package]]
|
||||||
|
name = "windows_x86_64_msvc"
|
||||||
|
version = "0.42.1"
|
||||||
|
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
|
checksum = "447660ad36a13288b1db4d4248e857b510e8c3a225c822ba4fb748c0aafecffd"
|
||||||
14
assignment-1b/Cargo.toml
Normal file
14
assignment-1b/Cargo.toml
Normal file
|
|
@ -0,0 +1,14 @@
|
||||||
|
[package]
|
||||||
|
name = "assignment-1b"
|
||||||
|
authors = ["Michael Zhang <zhan4854@umn.edu>"]
|
||||||
|
version = "0.1.0"
|
||||||
|
edition = "2021"
|
||||||
|
|
||||||
|
[dependencies]
|
||||||
|
anyhow = "1.0.68"
|
||||||
|
clap = { version = "4.1.4", features = ["derive"] }
|
||||||
|
derivative = "2.2.0"
|
||||||
|
nalgebra = "0.32.1"
|
||||||
|
num = { version = "0.4.0", features = ["serde"] }
|
||||||
|
ordered-float = "3.4.0"
|
||||||
|
rayon = "1.6.1"
|
||||||
45
assignment-1b/Makefile
Normal file
45
assignment-1b/Makefile
Normal file
|
|
@ -0,0 +1,45 @@
|
||||||
|
.PHONY: all clean
|
||||||
|
|
||||||
|
.PRECIOUS: $(EXAMPLES_PPM)
|
||||||
|
|
||||||
|
DOCKER := docker
|
||||||
|
ZIP := zip
|
||||||
|
PANDOC := pandoc
|
||||||
|
CONVERT := convert
|
||||||
|
|
||||||
|
HANDIN := hw1b.michael.zhang.zip
|
||||||
|
BINARY := ./assignment-1b
|
||||||
|
WRITEUP := writeup.pdf
|
||||||
|
SOURCES := $(shell find -name "*.rs")
|
||||||
|
|
||||||
|
EXAMPLES := $(shell find examples -name "*.txt")
|
||||||
|
EXAMPLES_PPM := $(patsubst %.txt,%.ppm,$(EXAMPLES))
|
||||||
|
EXAMPLES_PNG := $(patsubst %.txt,%.png,$(EXAMPLES))
|
||||||
|
|
||||||
|
all: $(HANDIN)
|
||||||
|
|
||||||
|
$(BINARY): $(SOURCES)
|
||||||
|
$(DOCKER) run \
|
||||||
|
--rm \
|
||||||
|
-v "$(shell pwd)":/usr/src/myapp \
|
||||||
|
-v cargo-registry:/usr/local/cargo \
|
||||||
|
--user "$(shell id -u)":"$(shell id -g)" \
|
||||||
|
-w /usr/src/myapp \
|
||||||
|
rust \
|
||||||
|
cargo build --release
|
||||||
|
mv target/release/assignment-1b $@
|
||||||
|
|
||||||
|
$(HANDIN): $(BINARY) $(WRITEUP) Makefile Cargo.toml Cargo.lock README.md $(EXAMPLES_PNG) $(EXAMPLES_PPM)
|
||||||
|
$(ZIP) -r $@ src examples $^
|
||||||
|
|
||||||
|
examples/%.ppm: examples/%.txt $(SOURCES)
|
||||||
|
cargo run -- -o $@ $<
|
||||||
|
|
||||||
|
examples/%.png: examples/%.ppm
|
||||||
|
convert $< $@
|
||||||
|
|
||||||
|
writeup.pdf: writeup.md $(EXAMPLES_PNG)
|
||||||
|
$(PANDOC) -o $@ $<
|
||||||
|
|
||||||
|
clean:
|
||||||
|
rm -f $(HANDIN) $(BINARY) $(WRITEUP) $(EXAMPLES_PPM) $(EXAMPLES_PNG)
|
||||||
25
assignment-1b/README.md
Normal file
25
assignment-1b/README.md
Normal file
|
|
@ -0,0 +1,25 @@
|
||||||
|
# Raycaster
|
||||||
|
|
||||||
|
## Bundle contents
|
||||||
|
|
||||||
|
Writeup is located at `/writeup.pdf`.
|
||||||
|
|
||||||
|
The binary can be found at `/assignment-1`. Run `./assignment-1 --help` to see
|
||||||
|
how to use it. The binary has been built using the Rust Docker image, which
|
||||||
|
should have an environment similar to CSELabs. If there is trouble running the
|
||||||
|
binary, try building from source, as documented below.
|
||||||
|
|
||||||
|
Examples are found in the `examples` directory. The text files are the input
|
||||||
|
sources, and the ppm files are the corresponding outputs. They have been
|
||||||
|
generated by running this program. For convenience, pngs have also been provided
|
||||||
|
using imagemagick.
|
||||||
|
|
||||||
|
## Building from source
|
||||||
|
|
||||||
|
The Makefile currently uses Docker to produce a more consistent build. If you
|
||||||
|
have a Rust+Cargo toolchain installed locally, it's also possible to build the
|
||||||
|
source using just:
|
||||||
|
|
||||||
|
cargo build --release
|
||||||
|
|
||||||
|
The binary will be found in `target/release`.
|
||||||
BIN
assignment-1b/assignment-1b
Executable file
BIN
assignment-1b/assignment-1b
Executable file
Binary file not shown.
12
assignment-1b/examples/cylinder.txt
Normal file
12
assignment-1b/examples/cylinder.txt
Normal file
|
|
@ -0,0 +1,12 @@
|
||||||
|
imsize 640 480
|
||||||
|
eye 0 0 15
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 60
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light -10 10 -3 0 0 0.4 0.4
|
||||||
|
light 10 10 -3 1 0.4 0 0.4
|
||||||
|
|
||||||
|
mtlcolor 0.5 1 0.5 0.2 0.4 0.8 0.2 0.4 0 10
|
||||||
|
cylinder -2 4 -3 0 0 5 1 4
|
||||||
23
assignment-1b/examples/ka-demo.txt
Normal file
23
assignment-1b/examples/ka-demo.txt
Normal file
|
|
@ -0,0 +1,23 @@
|
||||||
|
imsize 600 200
|
||||||
|
eye 0 0 15
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 90
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light 0 3 3 0 0.3 0.3 0.4
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0 0.4 0 1
|
||||||
|
sphere -10 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0.4 0 1
|
||||||
|
sphere -5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.4 0.4 0 1
|
||||||
|
sphere 0 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.6 0.4 0 1
|
||||||
|
sphere 5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.8 0.4 0 1
|
||||||
|
sphere 10 0 0 2
|
||||||
23
assignment-1b/examples/kd-demo.txt
Normal file
23
assignment-1b/examples/kd-demo.txt
Normal file
|
|
@ -0,0 +1,23 @@
|
||||||
|
imsize 600 200
|
||||||
|
eye 0 0 15
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 90
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light 0 3 3 0 0.3 0.3 0.4
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0 0 1
|
||||||
|
sphere -10 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0.2 0 1
|
||||||
|
sphere -5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0.4 0 1
|
||||||
|
sphere 0 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0.6 0 1
|
||||||
|
sphere 5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0.8 0 1
|
||||||
|
sphere 10 0 0 2
|
||||||
23
assignment-1b/examples/ks-demo.txt
Normal file
23
assignment-1b/examples/ks-demo.txt
Normal file
|
|
@ -0,0 +1,23 @@
|
||||||
|
imsize 600 200
|
||||||
|
eye 0 0 15
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 90
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light 0 3 3 0 0.3 0.3 0.4
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0 15
|
||||||
|
sphere -10 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.2 15
|
||||||
|
sphere -5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.4 15
|
||||||
|
sphere 0 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.6 15
|
||||||
|
sphere 5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.8 15
|
||||||
|
sphere 10 0 0 2
|
||||||
23
assignment-1b/examples/n-demo.txt
Normal file
23
assignment-1b/examples/n-demo.txt
Normal file
|
|
@ -0,0 +1,23 @@
|
||||||
|
imsize 600 200
|
||||||
|
eye 0 0 15
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 90
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light 0 3 3 0 0.3 0.3 0.4
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.4 2
|
||||||
|
sphere -10 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.4 6
|
||||||
|
sphere -5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.4 10
|
||||||
|
sphere 0 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.4 50
|
||||||
|
sphere 5 0 0 2
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.1 0.2 0.4 100
|
||||||
|
sphere 10 0 0 2
|
||||||
25
assignment-1b/examples/objects.txt
Normal file
25
assignment-1b/examples/objects.txt
Normal file
|
|
@ -0,0 +1,25 @@
|
||||||
|
imsize 640 480
|
||||||
|
eye 0 0 15
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 60
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light -10 10 -3 0 0 0.4 0.4
|
||||||
|
light 10 10 -3 1 0.4 0 0.4
|
||||||
|
|
||||||
|
mtlcolor 0 0.5 0.5 1 1 1 0.2 0.4 0 10
|
||||||
|
sphere -1 -2 -5 2
|
||||||
|
sphere 3 -5 -1 0.5
|
||||||
|
|
||||||
|
mtlcolor 0.5 0.5 1 0.4 0.4 0.4 0.2 0.4 0 10
|
||||||
|
sphere 1 2 -3 3
|
||||||
|
sphere -6 3 -4 1
|
||||||
|
|
||||||
|
mtlcolor 0.5 0 0.5 0.6 0.4 0.2 0.2 0.4 0 10
|
||||||
|
sphere 5 5 -1 1
|
||||||
|
sphere -6 -4 -8 7
|
||||||
|
cylinder -2 4 -3 0 0 5 1 4
|
||||||
|
|
||||||
|
mtlcolor 0.5 1 0.5 0.2 0.4 0.8 0.2 0.4 0 10
|
||||||
|
cylinder 5 1 -2 1 -2 1 1 2
|
||||||
12
assignment-1b/examples/sample-1.txt
Normal file
12
assignment-1b/examples/sample-1.txt
Normal file
|
|
@ -0,0 +1,12 @@
|
||||||
|
imsize 256 256
|
||||||
|
eye 0 0 0
|
||||||
|
viewdir 0 0 -1
|
||||||
|
hfov 90
|
||||||
|
updir 0 1 0
|
||||||
|
bkgcolor 0.1 0.1 0.1
|
||||||
|
|
||||||
|
light -2 3 -3 0 1 0.5 0.6
|
||||||
|
light 2 3 -3 1 0.5 0.5 1
|
||||||
|
|
||||||
|
mtlcolor 0 1 0 1 1 1 0.2 0.4 0 10
|
||||||
|
sphere 0 0 -5 2
|
||||||
41
assignment-1b/src/image.rs
Normal file
41
assignment-1b/src/image.rs
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
use std::io::{Result, Write};
|
||||||
|
|
||||||
|
use nalgebra::Vector3;
|
||||||
|
|
||||||
|
/// A pixel color represented by a red, green, and blue value in the range 0-1.
|
||||||
|
pub type Color = Vector3<f64>;
|
||||||
|
|
||||||
|
/// A representation of an image
|
||||||
|
pub struct Image {
|
||||||
|
/// Width in pixels
|
||||||
|
pub(crate) width: usize,
|
||||||
|
|
||||||
|
/// Height in pixels
|
||||||
|
pub(crate) height: usize,
|
||||||
|
|
||||||
|
/// Pixel data in row-major form.
|
||||||
|
pub(crate) data: Vec<Color>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Image {
|
||||||
|
/// Write the image in PPM format to a file.
|
||||||
|
pub fn write(&self, mut w: impl Write) -> Result<()> {
|
||||||
|
// Header
|
||||||
|
let header = format!("P3 {} {} 255\n", self.width, self.height);
|
||||||
|
w.write_all(header.as_bytes())?;
|
||||||
|
|
||||||
|
// Pixel data
|
||||||
|
assert_eq!(self.data.len(), self.width * self.height);
|
||||||
|
|
||||||
|
for pixel in self.data.iter() {
|
||||||
|
let pixel = pixel * 256.0;
|
||||||
|
let red = pixel.x as u8;
|
||||||
|
let green = pixel.y as u8;
|
||||||
|
let blue = pixel.z as u8;
|
||||||
|
let pixel = format!("{red} {green} {blue}\n");
|
||||||
|
w.write_all(pixel.as_bytes())?;
|
||||||
|
}
|
||||||
|
|
||||||
|
Ok(())
|
||||||
|
}
|
||||||
|
}
|
||||||
138
assignment-1b/src/input_file.rs
Normal file
138
assignment-1b/src/input_file.rs
Normal file
|
|
@ -0,0 +1,138 @@
|
||||||
|
use std::{fs::File, io::Read, path::Path};
|
||||||
|
|
||||||
|
use anyhow::Result;
|
||||||
|
use nalgebra::Vector3;
|
||||||
|
|
||||||
|
use crate::{
|
||||||
|
image::Color,
|
||||||
|
scene::{
|
||||||
|
cylinder::Cylinder,
|
||||||
|
data::{Light, LightKind, Material, Object, Scene},
|
||||||
|
sphere::Sphere,
|
||||||
|
},
|
||||||
|
};
|
||||||
|
|
||||||
|
/// Parse the input file into a scene
|
||||||
|
pub fn parse_input_file(path: impl AsRef<Path>) -> Result<Scene> {
|
||||||
|
let contents = {
|
||||||
|
let mut contents = String::new();
|
||||||
|
let mut file = File::open(path.as_ref())?;
|
||||||
|
file.read_to_string(&mut contents)?;
|
||||||
|
contents
|
||||||
|
};
|
||||||
|
|
||||||
|
let mut scene = Scene::default();
|
||||||
|
let mut material_color = None;
|
||||||
|
|
||||||
|
for line in contents.lines() {
|
||||||
|
let mut parts = line.split_whitespace();
|
||||||
|
let keyword = match parts.next() {
|
||||||
|
Some(v) => v,
|
||||||
|
None => continue,
|
||||||
|
};
|
||||||
|
|
||||||
|
if keyword == "imsize" {
|
||||||
|
let parts = parts
|
||||||
|
.map(|s| s.parse::<usize>().map_err(|e| e.into()))
|
||||||
|
.collect::<Result<Vec<_>>>()?;
|
||||||
|
if let [width, height] = parts[..] {
|
||||||
|
scene.image_width = width;
|
||||||
|
scene.image_height = height;
|
||||||
|
}
|
||||||
|
} else if keyword == "projection" {
|
||||||
|
if let Some("parallel") = parts.next() {
|
||||||
|
scene.parallel_projection = true;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// Do float parsing instead
|
||||||
|
else {
|
||||||
|
let parts = parts
|
||||||
|
.map(|s| s.parse::<f64>().map_err(|e| e.into()))
|
||||||
|
.collect::<Result<Vec<_>>>()?;
|
||||||
|
|
||||||
|
let read_vec3 = |start: usize| {
|
||||||
|
if parts.len() < start + 3 {
|
||||||
|
bail!("Vec3 requires 3 components.");
|
||||||
|
}
|
||||||
|
Ok(Vector3::new(
|
||||||
|
parts[start],
|
||||||
|
parts[start + 1],
|
||||||
|
parts[start + 2],
|
||||||
|
))
|
||||||
|
};
|
||||||
|
|
||||||
|
match keyword {
|
||||||
|
"eye" => scene.eye_pos = read_vec3(0)?,
|
||||||
|
"viewdir" => scene.view_dir = read_vec3(0)?,
|
||||||
|
"updir" => scene.up_dir = read_vec3(0)?,
|
||||||
|
|
||||||
|
"hfov" => scene.hfov = parts[0],
|
||||||
|
"bkgcolor" => scene.bkg_color = read_vec3(0)?,
|
||||||
|
|
||||||
|
"light" => {
|
||||||
|
let kind = match parts[3] as usize {
|
||||||
|
0 => LightKind::Directional {
|
||||||
|
direction: read_vec3(0)?,
|
||||||
|
},
|
||||||
|
1 => LightKind::Point {
|
||||||
|
location: read_vec3(0)?,
|
||||||
|
},
|
||||||
|
_ => bail!("Invalid w"),
|
||||||
|
};
|
||||||
|
let light = Light {
|
||||||
|
kind,
|
||||||
|
color: read_vec3(4)?,
|
||||||
|
};
|
||||||
|
scene.lights.push(light);
|
||||||
|
}
|
||||||
|
|
||||||
|
// mtlcolor Odr Odg Odb Osr Osg Osb ka kd ks n
|
||||||
|
"mtlcolor" => {
|
||||||
|
let diffuse_color = read_vec3(0)?;
|
||||||
|
let specular_color = read_vec3(3)?;
|
||||||
|
|
||||||
|
let material = Material {
|
||||||
|
diffuse_color,
|
||||||
|
specular_color,
|
||||||
|
k_a: parts[6],
|
||||||
|
k_d: parts[7],
|
||||||
|
k_s: parts[8],
|
||||||
|
exponent: parts[9],
|
||||||
|
};
|
||||||
|
|
||||||
|
let idx = scene.materials.len();
|
||||||
|
material_color = Some(idx);
|
||||||
|
scene.materials.push(material);
|
||||||
|
}
|
||||||
|
|
||||||
|
"sphere" => scene.objects.push(Object {
|
||||||
|
kind: Box::new(Sphere {
|
||||||
|
center: read_vec3(0)?,
|
||||||
|
radius: parts[3],
|
||||||
|
}),
|
||||||
|
material: match material_color {
|
||||||
|
Some(v) => v,
|
||||||
|
None => bail!("Each sphere must be preceded by a `mtlcolor` line"),
|
||||||
|
},
|
||||||
|
}),
|
||||||
|
|
||||||
|
"cylinder" => scene.objects.push(Object {
|
||||||
|
kind: Box::new(Cylinder {
|
||||||
|
center: read_vec3(0)?,
|
||||||
|
direction: read_vec3(3)?,
|
||||||
|
radius: parts[6],
|
||||||
|
length: parts[7],
|
||||||
|
}),
|
||||||
|
material: match material_color {
|
||||||
|
Some(v) => v,
|
||||||
|
None => bail!("Each sphere must be preceded by a `mtlcolor` line"),
|
||||||
|
},
|
||||||
|
}),
|
||||||
|
|
||||||
|
_ => bail!("Unknown keyword {keyword}"),
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
Ok(scene)
|
||||||
|
}
|
||||||
153
assignment-1b/src/main.rs
Normal file
153
assignment-1b/src/main.rs
Normal file
|
|
@ -0,0 +1,153 @@
|
||||||
|
#[macro_use]
|
||||||
|
extern crate anyhow;
|
||||||
|
#[macro_use]
|
||||||
|
extern crate derivative;
|
||||||
|
|
||||||
|
mod image;
|
||||||
|
mod input_file;
|
||||||
|
mod ray;
|
||||||
|
mod scene;
|
||||||
|
mod utils;
|
||||||
|
|
||||||
|
use std::fs::File;
|
||||||
|
use std::path::PathBuf;
|
||||||
|
|
||||||
|
use anyhow::Result;
|
||||||
|
use clap::Parser;
|
||||||
|
use rayon::prelude::{IntoParallelIterator, ParallelIterator};
|
||||||
|
|
||||||
|
use crate::image::Image;
|
||||||
|
use crate::input_file::parse_input_file;
|
||||||
|
use crate::ray::Ray;
|
||||||
|
|
||||||
|
/// Simple raycaster.
|
||||||
|
#[derive(Parser)]
|
||||||
|
#[clap(author, version, about, long_about = None)]
|
||||||
|
struct Opt {
|
||||||
|
/// Path to the input file to use.
|
||||||
|
#[clap()]
|
||||||
|
input_path: PathBuf,
|
||||||
|
|
||||||
|
/// Path to the output (defaults to the same file name as the input except
|
||||||
|
/// with an extension of .ppm)
|
||||||
|
#[clap(short = 'o', long = "output")]
|
||||||
|
output_path: Option<PathBuf>,
|
||||||
|
|
||||||
|
/// Force parallel projection to be used
|
||||||
|
#[clap(long = "parallel")]
|
||||||
|
force_parallel: bool,
|
||||||
|
|
||||||
|
/// Override distance from eye
|
||||||
|
#[clap(long = "distance", default_value = "1.0")]
|
||||||
|
distance: f64,
|
||||||
|
}
|
||||||
|
|
||||||
|
fn main() -> Result<()> {
|
||||||
|
let opt = Opt::parse();
|
||||||
|
let out_file = opt
|
||||||
|
.output_path
|
||||||
|
.unwrap_or_else(|| opt.input_path.with_extension("ppm"));
|
||||||
|
|
||||||
|
let mut scene = parse_input_file(&opt.input_path)?;
|
||||||
|
let distance = opt.distance;
|
||||||
|
|
||||||
|
if opt.force_parallel {
|
||||||
|
scene.parallel_projection = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Compute the viewing window
|
||||||
|
let view_window = scene.compute_viewing_window(distance);
|
||||||
|
|
||||||
|
// Translate image pixels to real-world 3d coords
|
||||||
|
let translate_pixel = {
|
||||||
|
let dx = view_window.upper_right - view_window.upper_left;
|
||||||
|
let pixel_base_x = dx / scene.image_width as f64;
|
||||||
|
|
||||||
|
let dy = view_window.lower_left - view_window.upper_left;
|
||||||
|
let pixel_base_y = dy / scene.image_height as f64;
|
||||||
|
|
||||||
|
move |px: usize, py: usize| {
|
||||||
|
let x_component = pixel_base_x * px as f64;
|
||||||
|
let y_component = pixel_base_y * py as f64;
|
||||||
|
|
||||||
|
// Without adding this, we would be getting the top-left of the pixel's
|
||||||
|
// rectangle. We want the center, so add half of the pixel size as
|
||||||
|
// well.
|
||||||
|
let center_offset = (pixel_base_x + pixel_base_y) / 2.0;
|
||||||
|
|
||||||
|
view_window.upper_left + x_component + y_component + center_offset
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
// Generate a parallel iterator for pixels
|
||||||
|
// The iterator preserves order and uses row-major order
|
||||||
|
let pixels_iter = (0..scene.image_height)
|
||||||
|
.into_par_iter()
|
||||||
|
.flat_map(|y| (0..scene.image_width).into_par_iter().map(move |x| (x, y)));
|
||||||
|
|
||||||
|
// Loop through every single pixel of the output file
|
||||||
|
let pixels = pixels_iter
|
||||||
|
.map(|(px, py)| {
|
||||||
|
let pixel_in_space = translate_pixel(px, py);
|
||||||
|
|
||||||
|
let ray_start = if scene.parallel_projection {
|
||||||
|
// For a parallel projection, we'll just take the view direction and
|
||||||
|
// subtract it from the target point. This means every single
|
||||||
|
// ray will be viewed from a point at infinity, rather than a single eye
|
||||||
|
// position.
|
||||||
|
let n = scene.view_dir.normalize();
|
||||||
|
let view_dir = n * distance;
|
||||||
|
pixel_in_space - view_dir
|
||||||
|
} else {
|
||||||
|
scene.eye_pos
|
||||||
|
};
|
||||||
|
|
||||||
|
let ray = Ray::from_endpoints(ray_start, pixel_in_space);
|
||||||
|
|
||||||
|
let intersections = scene
|
||||||
|
.objects
|
||||||
|
.iter()
|
||||||
|
.filter_map(|object| {
|
||||||
|
match object.kind.intersects_ray_at(&ray) {
|
||||||
|
Ok(Some(t)) => {
|
||||||
|
// Return both the t and the sphere, because we want to sort on
|
||||||
|
// the t but later retrieve attributes from the sphere
|
||||||
|
Some(Ok((t, object)))
|
||||||
|
}
|
||||||
|
Ok(None) => None,
|
||||||
|
Err(e) => Some(Err(e)),
|
||||||
|
}
|
||||||
|
})
|
||||||
|
.collect::<Result<Vec<_>>>()?;
|
||||||
|
|
||||||
|
// Sort the list of intersection times by the lowest one.
|
||||||
|
let earliest_intersection =
|
||||||
|
intersections.into_iter().min_by_key(|(t, _)| t.time);
|
||||||
|
|
||||||
|
Ok(match earliest_intersection {
|
||||||
|
// Take the object's material color
|
||||||
|
Some((intersection_context, object)) => {
|
||||||
|
scene.compute_pixel_color(object.material, intersection_context)
|
||||||
|
}
|
||||||
|
|
||||||
|
// There was no intersection, so this should default to the scene's
|
||||||
|
// background color
|
||||||
|
None => scene.bkg_color,
|
||||||
|
})
|
||||||
|
})
|
||||||
|
.collect::<Result<Vec<_>>>()?;
|
||||||
|
|
||||||
|
// Construct and emit image
|
||||||
|
let image = Image {
|
||||||
|
width: scene.image_width,
|
||||||
|
height: scene.image_height,
|
||||||
|
data: pixels,
|
||||||
|
};
|
||||||
|
|
||||||
|
{
|
||||||
|
let file = File::create(out_file)?;
|
||||||
|
image.write(file)?;
|
||||||
|
}
|
||||||
|
|
||||||
|
Ok(())
|
||||||
|
}
|
||||||
27
assignment-1b/src/ray.rs
Normal file
27
assignment-1b/src/ray.rs
Normal file
|
|
@ -0,0 +1,27 @@
|
||||||
|
use nalgebra::Vector3;
|
||||||
|
|
||||||
|
/// A normalized parametric Ray of the form (origin + direction * time)
|
||||||
|
///
|
||||||
|
/// That means at any time t: f64, the point represented by origin + direction *
|
||||||
|
/// time occurs on the ray.
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Ray {
|
||||||
|
pub origin: Vector3<f64>,
|
||||||
|
pub direction: Vector3<f64>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Ray {
|
||||||
|
/// Construct a ray from endpoints
|
||||||
|
pub fn from_endpoints(start: Vector3<f64>, end: Vector3<f64>) -> Self {
|
||||||
|
let delta = (end - start).normalize();
|
||||||
|
Ray {
|
||||||
|
origin: start,
|
||||||
|
direction: delta,
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Evaluate the ray at a certain point in time, yielding a point
|
||||||
|
pub fn eval(&self, time: f64) -> Vector3<f64> {
|
||||||
|
self.origin + self.direction * time
|
||||||
|
}
|
||||||
|
}
|
||||||
179
assignment-1b/src/scene/cylinder.rs
Normal file
179
assignment-1b/src/scene/cylinder.rs
Normal file
|
|
@ -0,0 +1,179 @@
|
||||||
|
use anyhow::Result;
|
||||||
|
use nalgebra::Vector3;
|
||||||
|
use ordered_float::NotNan;
|
||||||
|
|
||||||
|
use crate::ray::Ray;
|
||||||
|
use crate::utils::compute_rotation_matrix;
|
||||||
|
|
||||||
|
use super::data::{IntersectionContext, ObjectKind};
|
||||||
|
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Cylinder {
|
||||||
|
pub center: Vector3<f64>,
|
||||||
|
pub direction: Vector3<f64>,
|
||||||
|
pub radius: f64,
|
||||||
|
pub length: f64,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl ObjectKind for Cylinder {
|
||||||
|
/// Given a cylinder, returns the first time at which this ray intersects the
|
||||||
|
/// cylinder.
|
||||||
|
///
|
||||||
|
/// If there is no intersection point, returns None.
|
||||||
|
fn intersects_ray_at(
|
||||||
|
&self,
|
||||||
|
ray: &Ray,
|
||||||
|
) -> Result<Option<IntersectionContext>> {
|
||||||
|
// Determine rotation matrix for turning the cylinder upright along the
|
||||||
|
// Z-axis
|
||||||
|
let target_direction = Vector3::new(0.0, 0.0, 1.0);
|
||||||
|
let rotation_matrix =
|
||||||
|
compute_rotation_matrix(self.direction, target_direction)?;
|
||||||
|
let inverse_rotation_matrix =
|
||||||
|
rotation_matrix.try_inverse().ok_or_else(|| {
|
||||||
|
anyhow!("Rotation matrix for some reason does not have an inverse?")
|
||||||
|
})?;
|
||||||
|
|
||||||
|
// Transform all parameters according to this rotation matrix
|
||||||
|
let rotated_cylinder_center = rotation_matrix * self.center;
|
||||||
|
let rotated_ray_origin = rotation_matrix * ray.origin;
|
||||||
|
let rotated_ray_direction = rotation_matrix * ray.direction;
|
||||||
|
|
||||||
|
// Now that we know the cylinder is upright, we can start checking against
|
||||||
|
// the formula:
|
||||||
|
//
|
||||||
|
// (ox + t*rx - cx)^2 + (oy + t*ry - cy)^2 = r^2
|
||||||
|
//
|
||||||
|
// where o{xy} is the ray origin, r{xy} is the ray direction, and c{xy} is
|
||||||
|
// the cylinder center. The z will be taken care of after the fact. To
|
||||||
|
// solve, we must put it into the form At^2 + Bt + c = 0. The variables
|
||||||
|
// are:
|
||||||
|
//
|
||||||
|
// A: rx^2 + ry^2
|
||||||
|
// B: 2(rx(ox - cx) + ry(oy - cy))
|
||||||
|
// C: (cx - ox)^2 + (cy - oy)^2 - r^2
|
||||||
|
let (a, b, c) = {
|
||||||
|
let o = rotated_ray_origin;
|
||||||
|
let r = rotated_ray_direction;
|
||||||
|
let c = rotated_cylinder_center;
|
||||||
|
|
||||||
|
(
|
||||||
|
r.x.powi(2) + r.y.powi(2),
|
||||||
|
2.0 * (r.x * (o.x - c.x) + r.y * (o.y - c.y)),
|
||||||
|
(c.x - o.x).powi(2) + (c.y - o.y).powi(2) - self.radius.powi(2),
|
||||||
|
)
|
||||||
|
};
|
||||||
|
|
||||||
|
let discriminant = b * b - 4.0 * a * c;
|
||||||
|
|
||||||
|
let possible_side_solutions = match discriminant {
|
||||||
|
// Discriminant < 0, means the equation has no solutions.
|
||||||
|
d if d < 0.0 => vec![],
|
||||||
|
|
||||||
|
// Discriminant == 0
|
||||||
|
d if d == 0.0 => vec![-b / 2.0 * a],
|
||||||
|
|
||||||
|
// Discriminant > 0, 2 solutions available.
|
||||||
|
d if d > 0.0 => {
|
||||||
|
vec![
|
||||||
|
(-b + discriminant.sqrt()) / (2.0 * a),
|
||||||
|
(-b - discriminant.sqrt()) / (2.0 * a),
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
// Probably hit some NaN or Infinity value due to faulty inputs...
|
||||||
|
_ => bail!("Invalid determinant value: {discriminant}"),
|
||||||
|
};
|
||||||
|
|
||||||
|
// Filter out solutions that don't have a valid Z position.
|
||||||
|
let side_solutions = possible_side_solutions.into_iter().filter_map(|t| {
|
||||||
|
let ray_point = ray.eval(t);
|
||||||
|
let rotated_ray_point = rotation_matrix * ray_point;
|
||||||
|
let z = rotated_ray_point.z - rotated_cylinder_center.z;
|
||||||
|
|
||||||
|
// Check to see if z is between -len/2 and len/2
|
||||||
|
if z.abs() > self.length / 2.0 {
|
||||||
|
return None;
|
||||||
|
}
|
||||||
|
|
||||||
|
let time = NotNan::new(t).ok()?;
|
||||||
|
|
||||||
|
// The point on the center of the cylinder that corresponds to the z-axis
|
||||||
|
// point of the intersection
|
||||||
|
let center_at_z = {
|
||||||
|
let mut center_point = rotation_matrix * ray_point;
|
||||||
|
center_point.x = rotated_cylinder_center.x;
|
||||||
|
center_point.y = rotated_cylinder_center.y;
|
||||||
|
|
||||||
|
inverse_rotation_matrix * center_point
|
||||||
|
};
|
||||||
|
let normal = (ray_point - center_at_z).normalize();
|
||||||
|
|
||||||
|
Some(IntersectionContext {
|
||||||
|
time,
|
||||||
|
point: ray_point,
|
||||||
|
normal,
|
||||||
|
})
|
||||||
|
});
|
||||||
|
|
||||||
|
// We also need to add solutions for the two ends of the cylinder, which
|
||||||
|
// uses a similar method except backwards: check intersection points
|
||||||
|
// with the correct z-plane and then see if the points are within the
|
||||||
|
// circle.
|
||||||
|
//
|
||||||
|
// Luckily, this means we only need to care about one dimension at first,
|
||||||
|
// and don't need to perform the quadratic equation method above.
|
||||||
|
//
|
||||||
|
// oz + t * rz = cz +- (len / 2)
|
||||||
|
// t = (-oz + cz +- (len / 2)) / rz
|
||||||
|
let possible_z_intersections = {
|
||||||
|
let o = rotated_ray_origin;
|
||||||
|
let r = rotated_ray_direction;
|
||||||
|
let c = rotated_cylinder_center;
|
||||||
|
|
||||||
|
if r.z == 0.0 {
|
||||||
|
// No solutions here
|
||||||
|
vec![]
|
||||||
|
} else {
|
||||||
|
vec![
|
||||||
|
(-o.z + c.z + self.length / 2.0) / r.z,
|
||||||
|
(-o.z + c.z - self.length / 2.0) / r.z,
|
||||||
|
]
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
let end_solutions = possible_z_intersections.into_iter().filter_map(|t| {
|
||||||
|
let ray_point = ray.eval(t);
|
||||||
|
let rotated_point = rotation_matrix * ray_point;
|
||||||
|
|
||||||
|
// Filter out all the solutions where the intersection point does not lie
|
||||||
|
// in the circle
|
||||||
|
if rotated_point.x.powi(2) + rotated_point.y.powi(2) > self.radius.powi(2)
|
||||||
|
{
|
||||||
|
return None;
|
||||||
|
}
|
||||||
|
|
||||||
|
let normal_rotated =
|
||||||
|
Vector3::new(0.0, 0.0, rotated_point.z - rotated_cylinder_center.z)
|
||||||
|
.normalize();
|
||||||
|
let normal = inverse_rotation_matrix * normal_rotated;
|
||||||
|
|
||||||
|
let time = NotNan::new(t).ok()?;
|
||||||
|
Some(IntersectionContext {
|
||||||
|
time,
|
||||||
|
point: ray_point,
|
||||||
|
normal,
|
||||||
|
})
|
||||||
|
});
|
||||||
|
|
||||||
|
let solutions = side_solutions
|
||||||
|
.into_iter()
|
||||||
|
.chain(end_solutions.into_iter())
|
||||||
|
// Remove any t < 0, since that means it's behind the viewer and we
|
||||||
|
// can't see it.
|
||||||
|
.filter(|ctx| *ctx.time >= 0.0);
|
||||||
|
|
||||||
|
// Return the minimum solution
|
||||||
|
Ok(solutions.min_by_key(|ctx| ctx.time))
|
||||||
|
}
|
||||||
|
}
|
||||||
202
assignment-1b/src/scene/data.rs
Normal file
202
assignment-1b/src/scene/data.rs
Normal file
|
|
@ -0,0 +1,202 @@
|
||||||
|
use std::fmt::Debug;
|
||||||
|
|
||||||
|
use anyhow::Result;
|
||||||
|
use nalgebra::Vector3;
|
||||||
|
use ordered_float::NotNan;
|
||||||
|
|
||||||
|
use crate::image::Color;
|
||||||
|
use crate::ray::Ray;
|
||||||
|
|
||||||
|
pub trait ObjectKind: Debug + Send + Sync {
|
||||||
|
/// Determine where the ray intersects this object, returning the earliest
|
||||||
|
/// time this happens. Returns None if no intersection occurs.
|
||||||
|
///
|
||||||
|
/// Also known as Trace_Ray in the slides, except not the part where it calls
|
||||||
|
/// Shade_Ray.
|
||||||
|
fn intersects_ray_at(&self, ray: &Ray)
|
||||||
|
-> Result<Option<IntersectionContext>>;
|
||||||
|
}
|
||||||
|
|
||||||
|
/// An object in the scene
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Object {
|
||||||
|
pub kind: Box<dyn ObjectKind>,
|
||||||
|
|
||||||
|
/// Index into the scene's material color list
|
||||||
|
pub material: usize,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Rect {
|
||||||
|
pub upper_left: Vector3<f64>,
|
||||||
|
pub upper_right: Vector3<f64>,
|
||||||
|
pub lower_left: Vector3<f64>,
|
||||||
|
pub lower_right: Vector3<f64>,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Material {
|
||||||
|
pub diffuse_color: Vector3<f64>,
|
||||||
|
pub specular_color: Vector3<f64>,
|
||||||
|
|
||||||
|
pub k_a: f64,
|
||||||
|
pub k_d: f64,
|
||||||
|
pub k_s: f64,
|
||||||
|
pub exponent: f64,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub enum LightKind {
|
||||||
|
/// A point light source exists at a point and emits light in all directions
|
||||||
|
Point {
|
||||||
|
location: Vector3<f64>,
|
||||||
|
},
|
||||||
|
|
||||||
|
Directional {
|
||||||
|
direction: Vector3<f64>,
|
||||||
|
},
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Light {
|
||||||
|
pub kind: LightKind,
|
||||||
|
pub color: Vector3<f64>,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug, Default)]
|
||||||
|
pub struct Scene {
|
||||||
|
pub eye_pos: Vector3<f64>,
|
||||||
|
pub view_dir: Vector3<f64>,
|
||||||
|
pub up_dir: Vector3<f64>,
|
||||||
|
|
||||||
|
/// Horizontal field of view (in degrees)
|
||||||
|
pub hfov: f64,
|
||||||
|
pub parallel_projection: bool,
|
||||||
|
|
||||||
|
pub image_width: usize,
|
||||||
|
pub image_height: usize,
|
||||||
|
|
||||||
|
/// Background color
|
||||||
|
pub bkg_color: Color,
|
||||||
|
|
||||||
|
pub materials: Vec<Material>,
|
||||||
|
pub lights: Vec<Light>,
|
||||||
|
pub objects: Vec<Object>,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Derivative)]
|
||||||
|
#[derivative(Debug, PartialEq, PartialOrd, Ord)]
|
||||||
|
pub struct IntersectionContext {
|
||||||
|
/// The time of the intersection in the parametric ray
|
||||||
|
///
|
||||||
|
/// Unfortunately, IEEE floats in Rust don't have total ordering, because
|
||||||
|
/// NaNs violate ordering properties. The way to remedy this is to ensure we
|
||||||
|
/// don't have NaNs by wrapping it into this type, which then implements
|
||||||
|
/// total ordering.
|
||||||
|
pub time: NotNan<f64>,
|
||||||
|
|
||||||
|
/// The intersection point.
|
||||||
|
#[derivative(PartialEq = "ignore", Ord = "ignore")]
|
||||||
|
pub point: Vector3<f64>,
|
||||||
|
|
||||||
|
/// The normal vector protruding from the surface of the object at the
|
||||||
|
/// intersection point
|
||||||
|
#[derivative(PartialEq = "ignore", Ord = "ignore")]
|
||||||
|
pub normal: Vector3<f64>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Eq for IntersectionContext {}
|
||||||
|
|
||||||
|
impl Scene {
|
||||||
|
/// Determine the color that should be used to fill this pixel.
|
||||||
|
///
|
||||||
|
/// - material_idx is the index into the materials list.
|
||||||
|
/// - intersection_context contains information on vectors where the
|
||||||
|
/// intersection occurred
|
||||||
|
///
|
||||||
|
/// Also known as Shade_Ray in the slides.
|
||||||
|
pub fn compute_pixel_color(
|
||||||
|
&self,
|
||||||
|
material_idx: usize,
|
||||||
|
intersection_context: IntersectionContext,
|
||||||
|
) -> Color {
|
||||||
|
// TODO: Does it make sense to make this function fallible from an API
|
||||||
|
// design standpoint?
|
||||||
|
let material = match self.materials.get(material_idx) {
|
||||||
|
Some(v) => v,
|
||||||
|
None => return self.bkg_color,
|
||||||
|
};
|
||||||
|
|
||||||
|
let ambient_component = material.k_a * material.diffuse_color;
|
||||||
|
|
||||||
|
let diffuse_and_specular: Vector3<f64> = self
|
||||||
|
.lights
|
||||||
|
.iter()
|
||||||
|
.map(|light| {
|
||||||
|
// The vector pointing in the direction of the light
|
||||||
|
let light_direction = match light.kind {
|
||||||
|
LightKind::Point { location } => {
|
||||||
|
location - intersection_context.point
|
||||||
|
}
|
||||||
|
LightKind::Directional { direction } => direction,
|
||||||
|
}
|
||||||
|
.normalize();
|
||||||
|
|
||||||
|
let normal = intersection_context.normal.normalize();
|
||||||
|
let viewer_direction = self.eye_pos - intersection_context.point;
|
||||||
|
let halfway_direction =
|
||||||
|
((light_direction + viewer_direction) / 2.0).normalize();
|
||||||
|
|
||||||
|
let diffuse_component = material.k_d
|
||||||
|
* material.diffuse_color
|
||||||
|
* normal.dot(&light_direction).max(0.0);
|
||||||
|
|
||||||
|
let specular_component = material.k_s
|
||||||
|
* material.specular_color
|
||||||
|
* normal
|
||||||
|
.dot(&halfway_direction)
|
||||||
|
.max(0.0)
|
||||||
|
.powf(material.exponent);
|
||||||
|
|
||||||
|
diffuse_component + specular_component
|
||||||
|
})
|
||||||
|
.sum();
|
||||||
|
|
||||||
|
ambient_component + diffuse_and_specular
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Determine the boundaries of the viewing window in world coordinates
|
||||||
|
pub fn compute_viewing_window(&self, distance: f64) -> Rect {
|
||||||
|
// Compute viewing directions
|
||||||
|
let u = self.view_dir.cross(&self.up_dir).normalize();
|
||||||
|
let v = u.cross(&self.view_dir).normalize();
|
||||||
|
|
||||||
|
// Compute dimensions of viewing window based on field of view
|
||||||
|
let viewing_width = {
|
||||||
|
// Divide the angle in 2 since we are trying to use trig rules so we must
|
||||||
|
// get it from a right triangle
|
||||||
|
let half_hfov = self.hfov.to_radians() / 2.0;
|
||||||
|
|
||||||
|
// tan(hfov / 2) = w / 2d
|
||||||
|
let w_over_2d = half_hfov.tan();
|
||||||
|
|
||||||
|
// To find the viewing width we must multiply by 2d now
|
||||||
|
w_over_2d * 2.0 * distance
|
||||||
|
};
|
||||||
|
|
||||||
|
let aspect_ratio = self.image_width as f64 / self.image_height as f64;
|
||||||
|
let viewing_height = viewing_width / aspect_ratio;
|
||||||
|
|
||||||
|
// Compute viewing window corners
|
||||||
|
let n = self.view_dir.normalize();
|
||||||
|
#[rustfmt::skip] // Otherwise this line wraps over
|
||||||
|
let view_window = Rect {
|
||||||
|
upper_left: self.eye_pos + n * distance - u * (viewing_width / 2.0) + v * (viewing_height / 2.0),
|
||||||
|
upper_right: self.eye_pos + n * distance + u * (viewing_width / 2.0) + v * (viewing_height / 2.0),
|
||||||
|
lower_left: self.eye_pos + n * distance - u * (viewing_width / 2.0) - v * (viewing_height / 2.0),
|
||||||
|
lower_right: self.eye_pos + n * distance + u * (viewing_width / 2.0) - v * (viewing_height / 2.0),
|
||||||
|
};
|
||||||
|
|
||||||
|
view_window
|
||||||
|
}
|
||||||
|
}
|
||||||
3
assignment-1b/src/scene/mod.rs
Normal file
3
assignment-1b/src/scene/mod.rs
Normal file
|
|
@ -0,0 +1,3 @@
|
||||||
|
pub mod data;
|
||||||
|
pub mod sphere;
|
||||||
|
pub mod cylinder;
|
||||||
76
assignment-1b/src/scene/sphere.rs
Normal file
76
assignment-1b/src/scene/sphere.rs
Normal file
|
|
@ -0,0 +1,76 @@
|
||||||
|
use anyhow::Result;
|
||||||
|
use nalgebra::Vector3;
|
||||||
|
use ordered_float::NotNan;
|
||||||
|
|
||||||
|
use crate::{ray::Ray, utils::min_f64};
|
||||||
|
|
||||||
|
use super::data::{IntersectionContext, ObjectKind};
|
||||||
|
|
||||||
|
#[derive(Debug)]
|
||||||
|
pub struct Sphere {
|
||||||
|
pub center: Vector3<f64>,
|
||||||
|
pub radius: f64,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl ObjectKind for Sphere {
|
||||||
|
/// Given a sphere, returns the first time at which this ray intersects the
|
||||||
|
/// sphere.
|
||||||
|
///
|
||||||
|
/// If there is no intersection point, returns None.
|
||||||
|
fn intersects_ray_at(
|
||||||
|
&self,
|
||||||
|
ray: &Ray,
|
||||||
|
) -> Result<Option<IntersectionContext>> {
|
||||||
|
let a = ray.direction.x.powi(2)
|
||||||
|
+ ray.direction.y.powi(2)
|
||||||
|
+ ray.direction.z.powi(2);
|
||||||
|
let b = 2.0
|
||||||
|
* (ray.direction.x * (ray.origin.x - self.center.x)
|
||||||
|
+ ray.direction.y * (ray.origin.y - self.center.y)
|
||||||
|
+ ray.direction.z * (ray.origin.z - self.center.z));
|
||||||
|
let c = (ray.origin.x - self.center.x).powi(2)
|
||||||
|
+ (ray.origin.y - self.center.y).powi(2)
|
||||||
|
+ (ray.origin.z - self.center.z).powi(2)
|
||||||
|
- self.radius.powi(2);
|
||||||
|
let discriminant = b * b - 4.0 * a * c;
|
||||||
|
|
||||||
|
let time = match discriminant {
|
||||||
|
// Discriminant < 0, means the equation has no solutions.
|
||||||
|
d if d < 0.0 => None,
|
||||||
|
|
||||||
|
// Discriminant == 0
|
||||||
|
d if d == 0.0 => Some(-b / (2.0 * a)),
|
||||||
|
|
||||||
|
d if d > 0.0 => {
|
||||||
|
let solution_1 = (-b + discriminant.sqrt()) / (2.0 * a);
|
||||||
|
let solution_2 = (-b - discriminant.sqrt()) / (2.0 * a);
|
||||||
|
|
||||||
|
let solutions = [solution_1, solution_2]
|
||||||
|
.into_iter()
|
||||||
|
// Remove any t < 0, since that means it's behind the viewer and we
|
||||||
|
// can't see it.
|
||||||
|
.filter(|t| *t >= 0.0);
|
||||||
|
|
||||||
|
// Return the minimum solution
|
||||||
|
min_f64(solutions)
|
||||||
|
}
|
||||||
|
|
||||||
|
// Probably hit some NaN or Infinity value due to faulty inputs...
|
||||||
|
_ => unreachable!("Invalid determinant value: {discriminant}"),
|
||||||
|
};
|
||||||
|
|
||||||
|
let time = match time.and_then(|t| NotNan::new(t).ok()) {
|
||||||
|
Some(v) => v,
|
||||||
|
None => return Ok(None),
|
||||||
|
};
|
||||||
|
|
||||||
|
let point = ray.eval(*time);
|
||||||
|
let normal = (point - self.center).normalize();
|
||||||
|
|
||||||
|
Ok(Some(IntersectionContext {
|
||||||
|
time,
|
||||||
|
point,
|
||||||
|
normal,
|
||||||
|
}))
|
||||||
|
}
|
||||||
|
}
|
||||||
71
assignment-1b/src/utils.rs
Normal file
71
assignment-1b/src/utils.rs
Normal file
|
|
@ -0,0 +1,71 @@
|
||||||
|
use anyhow::Result;
|
||||||
|
use nalgebra::{Matrix3, Vector3};
|
||||||
|
use ordered_float::NotNan;
|
||||||
|
|
||||||
|
/// Finds the minimum of an iterator of f64s, ignoring any NaN values
|
||||||
|
pub fn min_f64<I>(i: I) -> Option<f64>
|
||||||
|
where
|
||||||
|
I: Iterator<Item = f64>,
|
||||||
|
{
|
||||||
|
i.filter_map(|i| NotNan::new(i).ok())
|
||||||
|
.min()
|
||||||
|
.map(|i| i.into_inner())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Finds the minimum of an iterator of f64s using the given predicate, ignoring
|
||||||
|
/// any NaN values
|
||||||
|
pub fn min_f64_by_key<I, F>(i: I, f: F) -> Option<f64>
|
||||||
|
where
|
||||||
|
I: Iterator<Item = f64>,
|
||||||
|
F: FnMut(&NotNan<f64>),
|
||||||
|
{
|
||||||
|
i.filter_map(|i| NotNan::new(i).ok())
|
||||||
|
.min_by_key(f)
|
||||||
|
.map(|i| i.into_inner())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Calculate the rotation matrix between the 2 given vectors
|
||||||
|
/// Based on the method here: https://math.stackexchange.com/a/897677
|
||||||
|
pub fn compute_rotation_matrix(
|
||||||
|
a: Vector3<f64>,
|
||||||
|
b: Vector3<f64>,
|
||||||
|
) -> Result<Matrix3<f64>> {
|
||||||
|
// Special case: if a and b are in the same direction, just return the identity matrix
|
||||||
|
if a.normalize() == b.normalize() {
|
||||||
|
return Ok(Matrix3::identity())
|
||||||
|
}
|
||||||
|
|
||||||
|
let cos_t = a.dot(&b);
|
||||||
|
let sin_t = a.cross(&b).norm();
|
||||||
|
|
||||||
|
let g = Matrix3::new(cos_t, -sin_t, 0.0, sin_t, cos_t, 0.0, 0.0, 0.0, 1.0);
|
||||||
|
|
||||||
|
// New basis vectors
|
||||||
|
let u = a;
|
||||||
|
let v = (b - a.dot(&b) * a).normalize();
|
||||||
|
let w = b.cross(&a);
|
||||||
|
|
||||||
|
// Not sure if this is required to be invertible?
|
||||||
|
let f_inverse = Matrix3::from_columns(&[u, v, w]);
|
||||||
|
let f = match f_inverse.try_inverse() {
|
||||||
|
Some(v) => v,
|
||||||
|
None => {
|
||||||
|
// So I ran into this case trying to compute the rotation matrix where one
|
||||||
|
// of the vector endpoints was (0, 0, 0). I'm pretty sure this case makes
|
||||||
|
// no sense in reality, so going to just error out here and screw
|
||||||
|
// recovering.
|
||||||
|
//
|
||||||
|
// println!("Failed to compute inverse matrix.");
|
||||||
|
// println!("- Initial: a = {a}, b = {b}");
|
||||||
|
// println!("- cos(t) = {cos_t}, sin(t) = {sin_t}");
|
||||||
|
// println!("- Basis: u = {u}, v = {v}, w = {w}");
|
||||||
|
bail!("Failed to compute inverse matrix of {f_inverse}\na = {a}\nb = {b}")
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
// if (f_inverse * g * f).norm() != 1.0 {
|
||||||
|
// bail!("WTF {}", (f_inverse * g * f).norm());
|
||||||
|
// }
|
||||||
|
|
||||||
|
Ok(f_inverse * g * f)
|
||||||
|
}
|
||||||
25
assignment-1b/writeup.md
Normal file
25
assignment-1b/writeup.md
Normal file
|
|
@ -0,0 +1,25 @@
|
||||||
|
---
|
||||||
|
geometry: margin=2cm
|
||||||
|
output: pdf_document
|
||||||
|
---
|
||||||
|
|
||||||
|
## Varying $k_a$
|
||||||
|
|
||||||
|
{width=240px}
|
||||||
|
|
||||||
|
## Varying $k_d$
|
||||||
|
|
||||||
|
{width=240px}
|
||||||
|
|
||||||
|
## Varying $k_s$
|
||||||
|
|
||||||
|
{width=240px}
|
||||||
|
|
||||||
|
## Varying $n$
|
||||||
|
|
||||||
|
{width=240px}
|
||||||
|
|
||||||
|
# Arbitrary Objects
|
||||||
|
|
||||||
|
{width=240px}
|
||||||
|
|
||||||
Loading…
Reference in a new issue